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Find the slope of the line in the graph.

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And just as a bit of a review, slope is just telling us how

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steep a line is.

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And the best way to view it, slope is equal to change in y

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over change in x.

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And for a line, this will always be constant.

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And sometimes you might see it written like this: you might

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see this triangle, that's a capital delta, that means

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change in, change in y over change in x.

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That's just a fancy way of saying change in y

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over change in x.

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So let's see what this change in y is for any change in x.

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So let's start at some point that seems pretty reasonable

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to read from this table right here, from this graph.

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So let's see, we're starting here-- let me do it in a more

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vibrant color-- so let's say we start at

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that point right there.

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And we want to go to another point that's pretty

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straightforward to read, so we can move to

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that point right there.

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We could literally pick any two points on this line.

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I'm just picking ones that are nice integer coordinates, so

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it's easy to read.

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So what is the change in y and what is the change in x?

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So first let's look at the change in x.

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So if we go from there to there, what is

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the change in x?

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My change in x is equal to what?

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Well, I can just count it out.

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I went 1 steps, 2 steps, 3 steps.

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My change in x is 3.

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And you could even see it from the x values.

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If I go from negative 3 to 0, I went up by 3.

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So my change in x is 3.

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So let me write this, change in x, delta x is equal to 3.

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And what's my change in y?

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Well, my change in y, I'm going from negative 3 up to

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negative 1, or you could just say 1, 2.

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So my change in y, is equal to positive 2.

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So let me write that down.

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Change in y is equal to 2.

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So what is my change in y for a change in x?

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Well, when my change in x was 3, my change in y is 2.

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So this is my slope.

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And one thing I want to do, I want to show you that I could

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have really picked any two points here.

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Let's say I didn't pick-- let me clear this out-- let's say

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I didn't pick those two points, let me pick some other

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points, and I'll even go in a different direction.

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I want to show you that you're going to get the same answer.

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Let's say I've used this as my starting point, and I want to

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go all the way over there.

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Well, let's think about the change in y first. So the

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change in y, I'm going down by how many units?

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1, 2, 3, 4 units, so my change in y, in this example, is

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negative 4.

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I went from 1 to negative 3, that's negative 4.

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That's my change in y.

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Change in y is equal to negative 4.

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Now what is my change in x?

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Well I'm going from this point, or from this x value,

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all the way-- let me do that in a different color-- all the

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way back like this.

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So I'm going to the left, so it's going to be a negative

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change in x, and I went 1, 2, 3, 4, 5, 6 units back.

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So my change in x is equal to negative 6.

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And you can even see I started it at x is equal to 3, and I

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went all the way to x is equal to negative 3.

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That's a change of negative 6.

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I went 6 to the left, or a change of negative 6.

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So what is my change in y over change in x?

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My change in y over change in x is equal to negative 4 over

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negative 6.

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The negatives cancel out and what's 4 over 6?

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Well, that's just 2 over 3.

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So it's the same value, you just have to be consistent.

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If this is my start point, I went down 4, and

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then I went back 6.

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Negative 4 over negative 6.

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If I viewed this as my starting point, I could say

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that I went up 4, so it would be a change in y would be 4,

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and then my change in x would be 6.

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And either way, once again, change in y over change in x

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is going to be 4 over 6, 2/3.

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So no matter which point you choose, as long as you kind of

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think about it in a consistent way, you're going to get the

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same value for slope.

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