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Find the slope of the line pictured on the graph.

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So the slope of a line is defined to be rise over run.

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Or you can also view it as change in y over change in x.

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And let me show you what that means.

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So let's start as some arbitrary point on this line.

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And they kind of highlight some of these points.

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So let's start at one of these points right over here.

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So if we wanted to start at one of these points. Let's say we want to change our x in the positive direction.

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So we want to go to the right. So let's say we want to go from this point to this point over here.

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How much do we have to move in x?

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So if we want to move in x, we have to go from this point to this point.

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We are going from -3 to 0.

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So we are going from -3 to 0.

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So our change in x, and this triangle, that's delta.

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That means change in. Our change in x is equal to 3.

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So our change in x over here is equal to 3.

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So what was our change in y when our change in x is equal to 3?

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Well when we moved from this point to this point, our x value changed by 3.

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But what happened to our y value?

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Well, our y value went down. It went from positive 3 to positive 2.

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Our y value went down by 1.

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So our change in y is equal to -1.

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So we rose -1. We actually went down.

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So our rise is -1 when our run, our change in x, is 3.

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The change in y over the change in x is -1 over 3.

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Or we could say that our slope is -1/3.

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It is -1/3.

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And I want to show you that we can do this with any two points on the line.

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We can even go further than 3 in the x direction.

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Let's go the other way. Let's start at this point right over here.

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And then move backwards to this point over here just to show you we will still get the same result.

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So to go from this point to that point, what is our change in x?

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So our change in x is this right over here.

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Our change in x is that distance right over there.

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We started at 3 and we went to -3. We went back 6.

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Over here, our change in x is equal to -6.

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We starting at this point now. So over here our change in x is -6.

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And then when our change in x is -6, when we start at this point and we move 6 back

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What is our change of y to get to that point?

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Well, our y-value went from 1, that was our y-value at this point,

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And then we go back to this point our y-value is 3.

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So now our y-value is 3. So what did we do?

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We moved up by 2. Our change in y is equal to 2.

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So over here, our change in y is equal to 2.

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Slope is change in y over change in x. Or, rise over run.

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Change in y is just rise. Change in x is just run, how much you're moving in the horizontal direction.

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So rise over run in this example here is going to be 2 over -6, which is the same thing as -1/3.

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And you could verify it for yourself.

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Take any of these two points. Start at one of these two points and figure out what is the run to get

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to the next point. And then what is the rise to get to the next point.

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And for any line, the slope won't change.

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Let me do it again.

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Over here, we had to move in the +3 direction. So that is our run.

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So this right here is +3. That's our run. But what's our rise?

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Well, we actually went down. So we have a negative rise. Our rise is -1.

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So we have -1 as our rise. We went down.

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Our run was +3. So our slope here is -1/3.