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Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So how much are those 2 guavas going to cost me? How much are those 2 guavas going to cost at full price? At full price. So a good place to start is to think about how much would those 6 guavas cost us at full price? This is the sale price right here. How much would those have cost me at full price? So let's do a little bit of algebra here. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So a good place to start is to think about how much would those 6 guavas cost us at full price? This is the sale price right here. How much would those have cost me at full price? So let's do a little bit of algebra here. Let me pick a suitable color for the algebra. So let's say that x is equal to the cost of 6 guavas at full price. So essentially if we take 30% off of this we should get $12.60. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So let's do a little bit of algebra here. Let me pick a suitable color for the algebra. So let's say that x is equal to the cost of 6 guavas at full price. So essentially if we take 30% off of this we should get $12.60. So let's do that. So if we have the full price of 6 guavas, we're going to take 30% off of that so that's the same thing as.30 or I could just write.3. I could ignore that 0 if I like. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So essentially if we take 30% off of this we should get $12.60. So let's do that. So if we have the full price of 6 guavas, we're going to take 30% off of that so that's the same thing as.30 or I could just write.3. I could ignore that 0 if I like. Actually let me write it like this. My wife is always bugging me to write 0s before decimals. So that's the full price of 6 guavas minus 0.30 times the full price of guavas. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | I could ignore that 0 if I like. Actually let me write it like this. My wife is always bugging me to write 0s before decimals. So that's the full price of 6 guavas minus 0.30 times the full price of guavas. So I'm literally just taking 30% off of the full price off of the full price. This is how we figure out the sale price. This is going to be equal to that $12.60 right there. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So that's the full price of 6 guavas minus 0.30 times the full price of guavas. So I'm literally just taking 30% off of the full price off of the full price. This is how we figure out the sale price. This is going to be equal to that $12.60 right there. That's going to be equal to $12.60. I just took 30% off of the full price. And now we just do algebra. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | This is going to be equal to that $12.60 right there. That's going to be equal to $12.60. I just took 30% off of the full price. And now we just do algebra. We can imagine there's a 1 in front. You know x is the same thing as 1x. So 1x minus 0.3x is going to be equal to.7x. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | And now we just do algebra. We can imagine there's a 1 in front. You know x is the same thing as 1x. So 1x minus 0.3x is going to be equal to.7x. So we get.7x or you could say.70 if you like. Same number. 0.7x is equal to $12.60. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So 1x minus 0.3x is going to be equal to.7x. So we get.7x or you could say.70 if you like. Same number. 0.7x is equal to $12.60. Once you get used to these problems, you might just skip straight to this step right here. You say, hey, 70% of the full price is equal to my sale price. I took 30% off. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | 0.7x is equal to $12.60. Once you get used to these problems, you might just skip straight to this step right here. You say, hey, 70% of the full price is equal to my sale price. I took 30% off. This is 70% of the full price. You might just skip to this step once you get used to these problems a little bit. Let's solve for x. Divide both sides by.7. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | I took 30% off. This is 70% of the full price. You might just skip to this step once you get used to these problems a little bit. Let's solve for x. Divide both sides by.7. x is equal to $12.60 divided by 0.7. We could use a calculator, but it's always good to get a little bit of practice dividing decimals. 0.7 goes into $12.60. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | Let's solve for x. Divide both sides by.7. x is equal to $12.60 divided by 0.7. We could use a calculator, but it's always good to get a little bit of practice dividing decimals. 0.7 goes into $12.60. Let's multiply both of these numbers by 10, which is what we do when we move both of their decimals one to the right. So the.7 becomes a 7. Ignore that right there. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | 0.7 goes into $12.60. Let's multiply both of these numbers by 10, which is what we do when we move both of their decimals one to the right. So the.7 becomes a 7. Ignore that right there. The $12.60 becomes $126. Put the decimal right there. We're ready to just do straight up long division. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | Ignore that right there. The $12.60 becomes $126. Put the decimal right there. We're ready to just do straight up long division. This is now a 7, not a.7. So 7 goes into 12 one time. 1 times 7 is 7. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | We're ready to just do straight up long division. This is now a 7, not a.7. So 7 goes into 12 one time. 1 times 7 is 7. 12 minus 7 is 5. Bring down the 6. 7 goes into 56 eight times. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | 1 times 7 is 7. 12 minus 7 is 5. Bring down the 6. 7 goes into 56 eight times. 8 times 7 is 56. Then we have no remainder. It's 18, and there's nothing behind the decimal point. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | 7 goes into 56 eight times. 8 times 7 is 56. Then we have no remainder. It's 18, and there's nothing behind the decimal point. In our case, it's $18. x is equal to $18. Remember what x was. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | It's 18, and there's nothing behind the decimal point. In our case, it's $18. x is equal to $18. Remember what x was. x was the full price of 6 guavas. x was the full price of 6 guavas. x is the full price of 6 guavas. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | Remember what x was. x was the full price of 6 guavas. x was the full price of 6 guavas. x is the full price of 6 guavas. Now the question is, how much will 2 guavas cost me the full price? Well, this is full price of 6. So you immediately could figure out what's the full price of 1 guava. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | x is the full price of 6 guavas. Now the question is, how much will 2 guavas cost me the full price? Well, this is full price of 6. So you immediately could figure out what's the full price of 1 guava. You divide 18 by 6. 18 divided by 6 is $3. That's $3 per guava at full price. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So you immediately could figure out what's the full price of 1 guava. You divide 18 by 6. 18 divided by 6 is $3. That's $3 per guava at full price. And they're asking us, we want 2 guavas. So 2 guavas is going to be 2 times $3. So this is going to be $6. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | That's $3 per guava at full price. And they're asking us, we want 2 guavas. So 2 guavas is going to be 2 times $3. So this is going to be $6. Another way you could have done it, you could have just said, hey, 6 at full price are going to cost me $18. 2 is 1 third of 6. So 1 third of $18 is $6. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So this is going to be $6. Another way you could have done it, you could have just said, hey, 6 at full price are going to cost me $18. 2 is 1 third of 6. So 1 third of $18 is $6. So just to give a quick review of what we did, we said the sale price on 6 guavas, $12.60. That's 30% off the full price. Or you could say this is 70% of the full price. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | So 1 third of $18 is $6. So just to give a quick review of what we did, we said the sale price on 6 guavas, $12.60. That's 30% off the full price. Or you could say this is 70% of the full price. And so you could say 30% x is the full price of 6 guavas. You could say the full price of 6 guavas minus 30% of the full price of 6 guavas is equal to $12.60. And that's equivalent to saying 70% of the full price is $12.60. |
Percent word problem example 1 Ratios, rates, and percentages 6th grade Khan Academy.mp3 | Or you could say this is 70% of the full price. And so you could say 30% x is the full price of 6 guavas. You could say the full price of 6 guavas minus 30% of the full price of 6 guavas is equal to $12.60. And that's equivalent to saying 70% of the full price is $12.60. Then we just solve this algebraically. Divide both sides by.7. And then we got x, the full price of 6 guavas is $18. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | We are asked to graph y is equal to 1 3rd x minus 2. Now, whenever you see an equation in this form, this is called slope intercept form. And the general way of writing it is y is equal to mx plus b. Where m is the slope, and here in this case m is equal to 1 3rd, so let me write that down. And b is the y intercept. So in this case b is equal to negative 2. And you know that b is the y intercept because we know that the y intercept occurs when x is equal to 0. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | Where m is the slope, and here in this case m is equal to 1 3rd, so let me write that down. And b is the y intercept. So in this case b is equal to negative 2. And you know that b is the y intercept because we know that the y intercept occurs when x is equal to 0. So if x is equal to 0 in either of these situations, this term just becomes 0 and y will be equal to b. So that's what we mean by b is the y intercept. So whenever you look at an equation in this form, it's actually fairly straightforward to graph this line. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | And you know that b is the y intercept because we know that the y intercept occurs when x is equal to 0. So if x is equal to 0 in either of these situations, this term just becomes 0 and y will be equal to b. So that's what we mean by b is the y intercept. So whenever you look at an equation in this form, it's actually fairly straightforward to graph this line. b is the y intercept, in this case it is negative 2. So that means that this line must intersect the y axis at y is equal to negative 2. So it's this point right here. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | So whenever you look at an equation in this form, it's actually fairly straightforward to graph this line. b is the y intercept, in this case it is negative 2. So that means that this line must intersect the y axis at y is equal to negative 2. So it's this point right here. Negative 1, negative 2. This is the point 0, negative 2. If you don't believe me, there's nothing magical about this. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | So it's this point right here. Negative 1, negative 2. This is the point 0, negative 2. If you don't believe me, there's nothing magical about this. Try evaluating or try solving for y when x is equal to 0. When x is equal to 0, this term cancels out and you're just left with y is equal to negative 2. So that's the y intercept right there. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | If you don't believe me, there's nothing magical about this. Try evaluating or try solving for y when x is equal to 0. When x is equal to 0, this term cancels out and you're just left with y is equal to negative 2. So that's the y intercept right there. Now, this 1 3rd tells us the slope of the line. How much do we change in y for any change in x? So this tells us that 1 3rd, so that right there is the slope. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | So that's the y intercept right there. Now, this 1 3rd tells us the slope of the line. How much do we change in y for any change in x? So this tells us that 1 3rd, so that right there is the slope. So it tells us that 1 3rd is equal to the change in y over the change in x. Or another way to think about it, if x changes by 3, then y will change by 1. So let me graph that. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | So this tells us that 1 3rd, so that right there is the slope. So it tells us that 1 3rd is equal to the change in y over the change in x. Or another way to think about it, if x changes by 3, then y will change by 1. So let me graph that. So we know that this point is on the graph. That's the y intercept. The slope tells us that if x changes by 3, so let me go 3 to the right, 1, 2, 3, that y will change by 1. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | So let me graph that. So we know that this point is on the graph. That's the y intercept. The slope tells us that if x changes by 3, so let me go 3 to the right, 1, 2, 3, that y will change by 1. So this must also be a point on the graph. And we could keep doing that. If x changes by 3, y changes by 1. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | The slope tells us that if x changes by 3, so let me go 3 to the right, 1, 2, 3, that y will change by 1. So this must also be a point on the graph. And we could keep doing that. If x changes by 3, y changes by 1. If x goes down by 3, y will go down by 1. If x goes down by 6, y will go down by 2. It's that same ratio. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | If x changes by 3, y changes by 1. If x goes down by 3, y will go down by 1. If x goes down by 6, y will go down by 2. It's that same ratio. So 1, 2, 3, 4, 5, 6, 1, 2. And you can see all of these points are on the line. And the line is the graph of this equation up here. |
Graph from slope-intercept equation example Algebra I Khan Academy.mp3 | It's that same ratio. So 1, 2, 3, 4, 5, 6, 1, 2. And you can see all of these points are on the line. And the line is the graph of this equation up here. So let me graph it. So it will look something like that. And you're done. |
Slope-intercept form Algebra I Khan Academy.mp3 | I could, let's see, I could subtract two x from both sides. I could write this as negative two x plus y is equal to three. I could manipulate it in ways where I get it to, and I'm not gonna do it right now, but this is another way of writing that same thing. Y minus five is equal to two times x minus one. You could actually simplify this and you could get either this equation here or that equation up on top. These are all equivalent. You can get from one to the other with logical algebraic operations. |
Slope-intercept form Algebra I Khan Academy.mp3 | Y minus five is equal to two times x minus one. You could actually simplify this and you could get either this equation here or that equation up on top. These are all equivalent. You can get from one to the other with logical algebraic operations. So there's an infinite number of ways to represent a given linear equation, but what I wanna focus on in this video is this representation in particular because this one is a very useful representation of a linear equation, and we'll see in future videos this one and this one can also be useful depending on what you are looking for, but we're gonna focus on this one. And this one right over here, it's often called slope-intercept form. Slope-intercept form. |
Slope-intercept form Algebra I Khan Academy.mp3 | You can get from one to the other with logical algebraic operations. So there's an infinite number of ways to represent a given linear equation, but what I wanna focus on in this video is this representation in particular because this one is a very useful representation of a linear equation, and we'll see in future videos this one and this one can also be useful depending on what you are looking for, but we're gonna focus on this one. And this one right over here, it's often called slope-intercept form. Slope-intercept form. And hopefully in a few minutes it will be obvious why it is called slope-intercept form. And before I explain that to you, let's just try to graph this thing. I'm gonna try to graph it. |
Slope-intercept form Algebra I Khan Academy.mp3 | Slope-intercept form. And hopefully in a few minutes it will be obvious why it is called slope-intercept form. And before I explain that to you, let's just try to graph this thing. I'm gonna try to graph it. I'm just gonna plot some points here. So x comma y, and I'm gonna pick some x values where it's easy to calculate the y values. So maybe the easiest is if x is equal to zero. |
Slope-intercept form Algebra I Khan Academy.mp3 | I'm gonna try to graph it. I'm just gonna plot some points here. So x comma y, and I'm gonna pick some x values where it's easy to calculate the y values. So maybe the easiest is if x is equal to zero. If x is equal to zero, then two times zero is zero. That term goes away, and you're only left with this term right over here, y is equal to three. Y is equal to three. |
Slope-intercept form Algebra I Khan Academy.mp3 | So maybe the easiest is if x is equal to zero. If x is equal to zero, then two times zero is zero. That term goes away, and you're only left with this term right over here, y is equal to three. Y is equal to three. And so if we were to plot this, actually let me start plotting it. So that is my y-axis. And let me do the x-axis. |
Slope-intercept form Algebra I Khan Academy.mp3 | Y is equal to three. And so if we were to plot this, actually let me start plotting it. So that is my y-axis. And let me do the x-axis. So that can be my x, oh that's not as straight as I would like it. So that looks pretty good. All right, that is my x-axis. |
Slope-intercept form Algebra I Khan Academy.mp3 | And let me do the x-axis. So that can be my x, oh that's not as straight as I would like it. So that looks pretty good. All right, that is my x-axis. And let me mark off some hash marks here. So this is x equals one, x equals two, x equals three, this is y equals, let me do this, y equals one, y equals two, y equals three, and obviously I can keep going, I can keep going. This would be y is equal to negative one. |
Slope-intercept form Algebra I Khan Academy.mp3 | All right, that is my x-axis. And let me mark off some hash marks here. So this is x equals one, x equals two, x equals three, this is y equals, let me do this, y equals one, y equals two, y equals three, and obviously I can keep going, I can keep going. This would be y is equal to negative one. This would be x is equal to negative one, negative two, negative three, so on and so forth. So this point right over here, zero comma three, this is x is zero, y is three. Well, the point that represents when x is equal to zero and y equals three, this is, we're right on the y-axis. |
Slope-intercept form Algebra I Khan Academy.mp3 | This would be y is equal to negative one. This would be x is equal to negative one, negative two, negative three, so on and so forth. So this point right over here, zero comma three, this is x is zero, y is three. Well, the point that represents when x is equal to zero and y equals three, this is, we're right on the y-axis. If there of a line going through it and this line contains this point, this is going to be the y-intercept. So one way to think about it, the reason why this is called slope-intercept form, is it's very easy to calculate the y-intercept. The y-intercept here is going to happen when it's written in this form, it's going to happen when x is equal to zero and y is equal to three. |
Slope-intercept form Algebra I Khan Academy.mp3 | Well, the point that represents when x is equal to zero and y equals three, this is, we're right on the y-axis. If there of a line going through it and this line contains this point, this is going to be the y-intercept. So one way to think about it, the reason why this is called slope-intercept form, is it's very easy to calculate the y-intercept. The y-intercept here is going to happen when it's written in this form, it's going to happen when x is equal to zero and y is equal to three. It's going to be this point right over here. So it's very easy to figure out the intercept, the y-intercept from this form. Now you might be saying, oh, well it's a slope-intercept form, it must also be easy to figure out the slope from this form. |
Slope-intercept form Algebra I Khan Academy.mp3 | The y-intercept here is going to happen when it's written in this form, it's going to happen when x is equal to zero and y is equal to three. It's going to be this point right over here. So it's very easy to figure out the intercept, the y-intercept from this form. Now you might be saying, oh, well it's a slope-intercept form, it must also be easy to figure out the slope from this form. And if you made that conclusion, you would be correct, and we're about to see that in a few seconds. So let's plot some more points here, and I'm just going to keep increasing x by one. So if you increase x by one, so we could write that our delta x, our change in x, delta Greek letter, this triangle's Greek letter delta represents change in, change in x here is one. |
Slope-intercept form Algebra I Khan Academy.mp3 | Now you might be saying, oh, well it's a slope-intercept form, it must also be easy to figure out the slope from this form. And if you made that conclusion, you would be correct, and we're about to see that in a few seconds. So let's plot some more points here, and I'm just going to keep increasing x by one. So if you increase x by one, so we could write that our delta x, our change in x, delta Greek letter, this triangle's Greek letter delta represents change in, change in x here is one. We just increased x by one. What's going to be our corresponding change in y? What's going to be our change in y? |
Slope-intercept form Algebra I Khan Academy.mp3 | So if you increase x by one, so we could write that our delta x, our change in x, delta Greek letter, this triangle's Greek letter delta represents change in, change in x here is one. We just increased x by one. What's going to be our corresponding change in y? What's going to be our change in y? So let's see, when x is equal to one, you have two times one plus three is going to be five. So our change in y is going to be two. Let's do that again. |
Slope-intercept form Algebra I Khan Academy.mp3 | What's going to be our change in y? So let's see, when x is equal to one, you have two times one plus three is going to be five. So our change in y is going to be two. Let's do that again. Let's increase our x by one, change in x is equal to one. So then if we go from, if we're going to increase by one, we're going to go from x equals one to x equals two, what's our corresponding change in y? Well, when x is equal to two, two times two is four plus three is seven. |
Slope-intercept form Algebra I Khan Academy.mp3 | Let's do that again. Let's increase our x by one, change in x is equal to one. So then if we go from, if we're going to increase by one, we're going to go from x equals one to x equals two, what's our corresponding change in y? Well, when x is equal to two, two times two is four plus three is seven. Well, our change in y, our change in y is equal to two. We went from five, when x went from one to two, y went from five to seven. So for every one that we increase x, y is increasing by two. |
Slope-intercept form Algebra I Khan Academy.mp3 | Well, when x is equal to two, two times two is four plus three is seven. Well, our change in y, our change in y is equal to two. We went from five, when x went from one to two, y went from five to seven. So for every one that we increase x, y is increasing by two. So for this linear equation, our change in y over change in x is always going to be, our change in y is two when our change in x is one, or it's equal to two. Or we could say that our slope is equal to two. And let's just graph this to make sure that we understand this. |
Slope-intercept form Algebra I Khan Academy.mp3 | So for every one that we increase x, y is increasing by two. So for this linear equation, our change in y over change in x is always going to be, our change in y is two when our change in x is one, or it's equal to two. Or we could say that our slope is equal to two. And let's just graph this to make sure that we understand this. So when x equals one, y is equal to five. And actually we're going to have to graph five up here. So when x is equal to one, y is equal to, and actually this is a little bit higher. |
Slope-intercept form Algebra I Khan Academy.mp3 | And let's just graph this to make sure that we understand this. So when x equals one, y is equal to five. And actually we're going to have to graph five up here. So when x is equal to one, y is equal to, and actually this is a little bit higher. Let me clean this up a little bit. So this one, let me erase that a little bit. Just like that. |
Slope-intercept form Algebra I Khan Academy.mp3 | So when x is equal to one, y is equal to, and actually this is a little bit higher. Let me clean this up a little bit. So this one, let me erase that a little bit. Just like that. So that's y is equal to four, and this is y is equal to five. So when x is one, y is equal to five. So it's that point right over there. |
Slope-intercept form Algebra I Khan Academy.mp3 | Just like that. So that's y is equal to four, and this is y is equal to five. So when x is one, y is equal to five. So it's that point right over there. So our line is going to look, you only need two points to define a line. Our line is going to look like, let me do this in this color right over here. Our line is going to look like, is going to look, is going to look something like, is going to look, let me see if I can, I didn't draw it completely at scale, but it's going to look something like this. |
Slope-intercept form Algebra I Khan Academy.mp3 | So it's that point right over there. So our line is going to look, you only need two points to define a line. Our line is going to look like, let me do this in this color right over here. Our line is going to look like, is going to look, is going to look something like, is going to look, let me see if I can, I didn't draw it completely at scale, but it's going to look something like this. This is the line, this is the line, y is equal to two x plus three. And we already figured out that its slope is equal to two. Our change, when our change in x is one, when our change in x is one, our change in y is two. |
Slope-intercept form Algebra I Khan Academy.mp3 | Our line is going to look like, is going to look, is going to look something like, is going to look, let me see if I can, I didn't draw it completely at scale, but it's going to look something like this. This is the line, this is the line, y is equal to two x plus three. And we already figured out that its slope is equal to two. Our change, when our change in x is one, when our change in x is one, our change in y is two. If our change in x was negative one, if our change in x was negative one, our change in y is negative two. And you could see that. If from zero we went down one, if we went to negative one, then what's our y going to be? |
Slope-intercept form Algebra I Khan Academy.mp3 | Our change, when our change in x is one, when our change in x is one, our change in y is two. If our change in x was negative one, if our change in x was negative one, our change in y is negative two. And you could see that. If from zero we went down one, if we went to negative one, then what's our y going to be? Two times negative one is negative two, plus three is one. So we see that the point one, or the point negative one comma one is on the line as well. So the slope here, our change in y or change in x, if we're going from, between any two points on this line, is always going to be two. |
Slope-intercept form Algebra I Khan Academy.mp3 | If from zero we went down one, if we went to negative one, then what's our y going to be? Two times negative one is negative two, plus three is one. So we see that the point one, or the point negative one comma one is on the line as well. So the slope here, our change in y or change in x, if we're going from, between any two points on this line, is always going to be two. But where did you see two in this original equation? Well, you see the two right over here. And when you write something in slope intercept form, where you explicitly solve for y, y is equal to some constant times x to the first power, plus some other constant, the second one is going to be your intercept, your y, or it's going to be a way to figure out the y intercept. |
Slope-intercept form Algebra I Khan Academy.mp3 | So the slope here, our change in y or change in x, if we're going from, between any two points on this line, is always going to be two. But where did you see two in this original equation? Well, you see the two right over here. And when you write something in slope intercept form, where you explicitly solve for y, y is equal to some constant times x to the first power, plus some other constant, the second one is going to be your intercept, your y, or it's going to be a way to figure out the y intercept. The intercept itself is this point, the point at which the line intersects the y axis. And then this two is going to represent your slope. And that makes sense, because every time you increase x by one, you're going to multiply that by two, so you're going to increase y by two. |
Slope-intercept form Algebra I Khan Academy.mp3 | And when you write something in slope intercept form, where you explicitly solve for y, y is equal to some constant times x to the first power, plus some other constant, the second one is going to be your intercept, your y, or it's going to be a way to figure out the y intercept. The intercept itself is this point, the point at which the line intersects the y axis. And then this two is going to represent your slope. And that makes sense, because every time you increase x by one, you're going to multiply that by two, so you're going to increase y by two. So this is just a kind of a, get your feet wet with the idea of slope intercept form, but you'll see, at least for me, this is the easiest form for me to think about what the graph of something looks like. Because if you were given another linear equation, let's say y is equal to negative x, negative x plus two. Well, immediately you say, okay, look, my y intercept is going to be the point zero comma two, so I'm going to intersect the y axis right at that point. |
Slope-intercept form Algebra I Khan Academy.mp3 | And that makes sense, because every time you increase x by one, you're going to multiply that by two, so you're going to increase y by two. So this is just a kind of a, get your feet wet with the idea of slope intercept form, but you'll see, at least for me, this is the easiest form for me to think about what the graph of something looks like. Because if you were given another linear equation, let's say y is equal to negative x, negative x plus two. Well, immediately you say, okay, look, my y intercept is going to be the point zero comma two, so I'm going to intersect the y axis right at that point. And then I have a slope of, the coefficient here is really just negative one. So I have a slope of negative one. So as we increase x by one, we're going to decrease y by one. |
Slope-intercept form Algebra I Khan Academy.mp3 | Well, immediately you say, okay, look, my y intercept is going to be the point zero comma two, so I'm going to intersect the y axis right at that point. And then I have a slope of, the coefficient here is really just negative one. So I have a slope of negative one. So as we increase x by one, we're going to decrease y by one. Increase x by one, you're going to decrease y by one. If you increase x by two, you're going to decrease y by two. And so our line is going to look something like this. |
Slope-intercept form Algebra I Khan Academy.mp3 | So as we increase x by one, we're going to decrease y by one. Increase x by one, you're going to decrease y by one. If you increase x by two, you're going to decrease y by two. And so our line is going to look something like this. Let me see if I can draw it relatively neatly. It's going to look something, it's, let me, I can do it a little bit better than that. It's because my graph paper is hand-drawn. |
Slope-intercept form Algebra I Khan Academy.mp3 | And so our line is going to look something like this. Let me see if I can draw it relatively neatly. It's going to look something, it's, let me, I can do it a little bit better than that. It's because my graph paper is hand-drawn. It's not ideal. But I think you get, you get the point. It's going to look something like that. |
Slope-intercept form Algebra I Khan Academy.mp3 | It's because my graph paper is hand-drawn. It's not ideal. But I think you get, you get the point. It's going to look something like that. So from slope-intercept form, very easy to figure out what the y intercept is, and very easy to figure out the slope. The slope here, slope here is negative one. That's this negative one right over here. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | Solve for a and check your solution. We have a plus 5 is equal to 54. Now all this is saying is that we have some number, some variable a, and if I add 5 to it, I will get 54. And you might be able to do this in your head, but we're going to do it a little bit more systematically, because that'll be helpful for you when we do more complicated problems. So in general, whenever you have an equation like this, we want to have the variable. We want this a all by itself on one side of the equation. We want to isolate it. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | And you might be able to do this in your head, but we're going to do it a little bit more systematically, because that'll be helpful for you when we do more complicated problems. So in general, whenever you have an equation like this, we want to have the variable. We want this a all by itself on one side of the equation. We want to isolate it. It's already on the left-hand side, so let's try to get rid of everything else on the left-hand side. Well, the only other thing on the left-hand side is this positive 5. Well, the best way to get rid of a plus 5 or of a positive 5 is to subtract 5. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | We want to isolate it. It's already on the left-hand side, so let's try to get rid of everything else on the left-hand side. Well, the only other thing on the left-hand side is this positive 5. Well, the best way to get rid of a plus 5 or of a positive 5 is to subtract 5. So let's subtract 5. But remember, this says a plus 5 is equal to 54. If we want the equality to still hold, anything we do to the left-hand side of this equation, we have to do to the right side of the equation. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | Well, the best way to get rid of a plus 5 or of a positive 5 is to subtract 5. So let's subtract 5. But remember, this says a plus 5 is equal to 54. If we want the equality to still hold, anything we do to the left-hand side of this equation, we have to do to the right side of the equation. So we also have to subtract 54 from the right. So we have a plus 5 minus 5. Well, that's just going to be a plus 0, because you add 5 and you subtract 5, they cancel out. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | If we want the equality to still hold, anything we do to the left-hand side of this equation, we have to do to the right side of the equation. So we also have to subtract 54 from the right. So we have a plus 5 minus 5. Well, that's just going to be a plus 0, because you add 5 and you subtract 5, they cancel out. So a plus 0 is just a. And then 54 minus 5, that is 49. And we're done. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | Well, that's just going to be a plus 0, because you add 5 and you subtract 5, they cancel out. So a plus 0 is just a. And then 54 minus 5, that is 49. And we're done. We have solved for a. a is equal to 49. And now we can check it. And we can check it by just substituting 49 back for a in our original equation. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | And we're done. We have solved for a. a is equal to 49. And now we can check it. And we can check it by just substituting 49 back for a in our original equation. So instead of writing a plus 5 is equal to 54, let's see if 49 plus 5 is equal to 54. So we're just substituting it back in. 49 plus 5 is equal to 54. |
Example of solving a one-step equation Linear equations Algebra I Khan Academy.mp3 | And we can check it by just substituting 49 back for a in our original equation. So instead of writing a plus 5 is equal to 54, let's see if 49 plus 5 is equal to 54. So we're just substituting it back in. 49 plus 5 is equal to 54. We're trying to check this. 49 plus 5 is 54. And that, indeed, is equal to 54. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | Now take the product of negative 8 and that expression and then add 6. So let's do it step by step. First we're going to have this expression, negative 5 plus something. So it's going to be negative 5 plus the quantity of 4 times x. The quantity of 4 times x, well that's just going to be 4x. So it's going to be negative 5 plus 4x. So that's this expression up here. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | So it's going to be negative 5 plus the quantity of 4 times x. The quantity of 4 times x, well that's just going to be 4x. So it's going to be negative 5 plus 4x. So that's this expression up here. Now take the product of negative 8. So we're going to take negative 8 and we're going to multiply the product of negative 8 and that expression. So we're going to take negative 8 and multiply it. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | So that's this expression up here. Now take the product of negative 8. So we're going to take negative 8 and we're going to multiply the product of negative 8 and that expression. So we're going to take negative 8 and multiply it. So that expression is this thing right over here. So the product, if we say the product of negative 8 and that expression, it's going to be negative 8 times that expression. That expression is negative 5 plus 4x. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | So we're going to take negative 8 and multiply it. So that expression is this thing right over here. So the product, if we say the product of negative 8 and that expression, it's going to be negative 8 times that expression. That expression is negative 5 plus 4x. So that's negative 8, that's that expression. The product of the two, so we could put a multiplication sign there or we could just leave that out. In implicit it would mean multiplication. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | That expression is negative 5 plus 4x. So that's negative 8, that's that expression. The product of the two, so we could put a multiplication sign there or we could just leave that out. In implicit it would mean multiplication. Take the product of negative 8 and that expression and then add 6. So that's and then add 6. So that would be then adding 6 right over here. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | In implicit it would mean multiplication. Take the product of negative 8 and that expression and then add 6. So that's and then add 6. So that would be then adding 6 right over here. So we could write it as negative 8, open parentheses, negative 5 plus 4x and then add 6. Let's do one more. First consider the expression, the sum of 7 and, so that's going to be 7 plus something, and the product of negative 2 and x. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | So that would be then adding 6 right over here. So we could write it as negative 8, open parentheses, negative 5 plus 4x and then add 6. Let's do one more. First consider the expression, the sum of 7 and, so that's going to be 7 plus something, and the product of negative 2 and x. The product of negative 2 and x is negative 2x. Negative 2x, so 7 plus negative 2x. We could write that as 7 minus 2x. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | First consider the expression, the sum of 7 and, so that's going to be 7 plus something, and the product of negative 2 and x. The product of negative 2 and x is negative 2x. Negative 2x, so 7 plus negative 2x. We could write that as 7 minus 2x. So this is equal to 7 minus 2x. These are the same expression. What expression would be 4 plus, so now we're saying 4 plus, 4 plus the quantity of 2 times that expression. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | We could write that as 7 minus 2x. So this is equal to 7 minus 2x. These are the same expression. What expression would be 4 plus, so now we're saying 4 plus, 4 plus the quantity of 2 times that expression. So it's going to be 4 plus some quantity, 4 plus the quantity, I'll put that in parentheses, the quantity of 2 times, do this in magenta, of 2 times that expression or in yellow. 2 times that expression, that, let me do this in blue, that expression is this thing right over here. So the 4 plus the quantity of 2 times that expression, 2 times 7 minus 2x. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | What expression would be 4 plus, so now we're saying 4 plus, 4 plus the quantity of 2 times that expression. So it's going to be 4 plus some quantity, 4 plus the quantity, I'll put that in parentheses, the quantity of 2 times, do this in magenta, of 2 times that expression or in yellow. 2 times that expression, that, let me do this in blue, that expression is this thing right over here. So the 4 plus the quantity of 2 times that expression, 2 times 7 minus 2x. And we are done. |
How to write algebraic expressions with parentheses Algebra I Khan Academy.mp3 | So the 4 plus the quantity of 2 times that expression, 2 times 7 minus 2x. And we are done. |