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Introduction Video: Finding Slope from a Graph

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Introduction Video: Finding Slope from a Graph

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Video to introduce finding slope from a graph.

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Find the slope of the line in the graph. And just as a bit of a review, slope is just telling us how steep a line is. And the best way to view it, slope is equal to change in y over change in x. And for a line, this will always be constant. And sometimes you might see it written like this: you might see this triangle, that's a capital delta, that means change in, change in y over change in x. That's just a fancy way of saying change in y over change in x. So let's see what this change in y is for any change in x. So let's start at some point that seems pretty reasonable to read from this table right here, from this graph. So let's see, we're starting here-- let me do it in a more vibrant color-- so let's say we start at that point right there. And we want to go to another point that's pretty straightforward to read, so we can move to that point right there. We could literally pick any two points on this line. I'm just picking ones that are nice integer coordinates, so it's easy to read. So what is the change in y and what is the change in x? So first let's look at the change in x. So if we go from there to there, what is the change in x? My change in x is equal to what? Well, I can just count it out. I went 1 steps, 2 steps, 3 steps. My change in x is 3. And you could even see it from the x values. If I go from negative 3 to 0, I went up by 3. So my change in x is 3. So let me write this, change in x, delta x is equal to 3. And what's my change in y? Well, my change in y, I'm going from negative 3 up to negative 1, or you could just say 1, 2. So my change in y, is equal to positive 2. So let me write that down. Change in y is equal to 2. So what is my change in y for a change in x? Well, when my change in x was 3, my change in y is 2. So this is my slope. And one thing I want to do, I want to show you that I could have really picked any two points here. Let's say I didn't pick-- let me clear this out-- let's say I didn't pick those two points, let me pick some other points, and I'll even go in a different direction. I want to show you that you're going to get the same answer. Let's say I've used this as my starting point, and I want to go all the way over there. Well, let's think about the change in y first. So the change in y, I'm going down by how many units? 1, 2, 3, 4 units, so my change in y, in this example, is negative 4. I went from 1 to negative 3, that's negative 4. That's my change in y. Change in y is equal to negative 4. Now what is my change in x? Well I'm going from this point, or from this x value, all the way-- let me do that in a different color-- all the way back like this. So I'm going to the left, so it's going to be a negative change in x, and I went 1, 2, 3, 4, 5, 6 units back. So my change in x is equal to negative 6. And you can even see I started it at x is equal to 3, and I went all the way to x is equal to negative 3. That's a change of negative 6. I went 6 to the left, or a change of negative 6. So what is my change in y over change in x? My change in y over change in x is equal to negative 4 over negative 6. The negatives cancel out and what's 4 over 6? Well, that's just 2 over 3. So it's the same value, you just have to be consistent. If this is my start point, I went down 4, and then I went back 6. Negative 4 over negative 6. If I viewed this as my starting point, I could say that I went up 4, so it would be a change in y would be 4, and then my change in x would be 6. And either way, once again, change in y over change in x is going to be 4 over 6, 2/3. So no matter which point you choose, as long as you kind of think about it in a consistent way, you're going to get the same value for slope.

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Finding slope from graph | Algebra (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Introduction Video: Finding Slope from Two Points

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Introduction Video: Finding Slope from Two Points

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Example Video and practice problems

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Worked example: slope from two points (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Catchy song about graphing slope

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Graph Shop - Graphing Lines Thrift Shop Parody

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This catchy song is a great introduction to what slope is and how to find it.

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Practice finding Slope of a graph. The questions get harder as your score goes up.

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IXL | Find the slope of a graph | 8th grade math

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Improve your math knowledge with free questions in "Find the slope of a graph" and thousands of other math skills.

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Practice finding slope from two points. The questions progressively get harder as your score goes up.

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IXL | Find the slope from two points | 8th grade math

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Improve your math knowledge with free questions in "Find the slope from two points" and thousands of other math skills.

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Practice graphing a line from an equation in slope-intercept form. Students have to know how to create a graph from an equation.

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IXL | Graph a line from an equation in slope-intercept form | 8th grade math

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Improve your math knowledge with free questions in "Graph a line from an equation in slope-intercept form" and thousands of other math skills.

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Practice writing an equation from a graph. Students have to know how to write an equation given a graph.

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IXL | Write a linear equation from a graph | 8th grade math

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Improve your math knowledge with free questions in "Write a linear equation from a graph" and thousands of other math skills.

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Introduction Video: Finding Slope from a Table

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Introduction Video: Finding Slope from a Table

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Video and Practice problems finding slope from a table.

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- [Instructor] We are asked, what is the slope of the line that contains these points? So pause this video and see if you can work through this on your own before we do it together. Alright, now let's do it together, and let's just remind ourselves what slope is. Slope is equal to change in y, this is the Greek letter delta, look likes a triangle, but it's shorthand for change in y over change in x. Sometimes you would see it written as y2 minus y1 over x2 minus x1 where you could kind of view x1 y1 as the starting point and x2 y2 as the ending point. So let's just pick two xy pairs here, and we can actually pick any two if we can assume that this is actually describing a line. So we might as well just pick the first two. So let's say that's our starting point and that's our finishing point. So what is our change in x here? So we're going from two to three, so our change in x is equal to three minus two which is equal to one, and you can see that to go from two to three you're just adding one. And what's our change in y? Our change in y is our finishing y one minus our starting y four, which is equal to negative three. And you could of, you didn't even have to do this math, you would have been able to see to go from two to three you added one, and to go from four to one, you have to subtract three. For there we have all the information we need. What is change in y over change in x? Well, it's going to be, our change in y is negative three and our change in x is one. So our slope is negative three divided by one is negative three. Let's do another example. Here we are asked, what is the slope of the line that contains these points? So pause this video and see if you can figure it out or pause the video again and see if you can figure it out. Alright, so remember, slope is equal to change in y over change in x. And we should be able to pick any two of these pairs in order to figure that out if we assume that this is indeed a line. Well, just for variety, let's pick these middle two pairs. So what's our change in x? To go from one to five, we added four. And what's our change in y? To go from seven to 13, we added six. So our change in y is six when our change in x is four. And I got the signs right, in both case it's a positive. When x increases, y increased as well. So our slope is six fourths, and we could rewrite that if we like. Both six and four are divisible by two, so let be divide both the numerator and the denominator by two and we get three halves, and we're done.

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Calculating slope from tables (video) | Khan Academy

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Instructor] We are asked, what is the slope of the line that contains these points? So pause this video and see if you can work through this on your own before we do it together. Alright, now let's do it together, and let's just remind ourselves what slope is.

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Review Video of the Types of Slope

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Review: The 4 Types of Slope of a Line (⤢⤡⟷↕)

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Slope of a Graph, Table, and Two Points Review

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Slope of a Graph, Table, and Two Points Review