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All right, what I'd like to do is show you guys how to find the rate of change from a graph.
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And what way I was a linear graph here, and when we're talking about rate of change,
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if you guys remember, we wrote down the definition of rate change.
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The definition of rate of change is it's a ratio of the change in two quantities.
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And when you're dealing with a linear graph or at the table, or between two points,
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our two quantities are giving you our x and y values.
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So what we call the rate of change of x and y values is what we call slope.
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Now, I'm just going to write this down here.
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So slope is the ratio of the change, and y values over x values.
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Now you guys say, well, all right, we're going to have this lie and I have these two points.
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Remember, a point always comes in the form x, y.
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So here's my x is negative 2, my y is 0.
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Over here, x is 2, y is negative 3.
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And the one example I like to keep mine going through is if there's not much change,
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what do you mean by change?
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How do you calculate the change?
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Well, if I had $20 yesterday, and I only have $2 today, what was the change in the
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money I had?
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And the change in the money I had was 18.
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Or yes, I lost 18, so it'd be a negative 18.
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But the change, what I did was, I took a much money I had, which was 20, and I subtracted
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2.
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So when you're trying to find the change, you're finding the difference.
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So you're always going to use subtraction.
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So I want to find the change in my y values.
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I need to subtract them.
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So I'm going to say, well, this y value is 3.
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So I'm going to say slope.
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And we're going to get into the general formula for slope in a little bit.
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But the general formula for this is going to be negative 3.
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That's one y value.
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Minus my other y value, which is 0.
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Over the change in my x value, which is 2 minus negative 2.
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Now, one thing to notice is negative 3 minus 0 is obviously going to be negative 3.
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And 2 minus negative 2, those both become positive.
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And we get 4.
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So it's negative 3.
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Now, if you're still a little bit uneasy about doing it algebraically, when given
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a graph, you're allowed a couple of different ways to solve this problem.
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So one way we can do this is we can look between these two points.
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And we say, if I was going to read the graph from left to right, how might change in my
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y-cordance?
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So from left to right, I'm going down how far.
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And you say, well, you're going down 1, 2, 3.
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So you say you're going down negative 3.
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And then from left to right, how far am I going over?
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And you say you're going over 1, 2, 3, 4.
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So therefore, my slope is negative 3 over 4.
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You could also go from right to left.
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So if I'm going right to left, that means I'm going up 3 and to the left negative 4.
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So it'd be the change in y was 3.
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So this would be 3 over negative 4.
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And these are the equivalent.
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It doesn't matter what you say.
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And I'll show you guys a quick little example.
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Why are they equivalent?
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Well, 8 divided by negative 2 is equal to negative 8 divided by 2.
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Because that's negative 4 equals negative 4.
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OK?
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So that's why these two slopes are equivalent.
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The only difference is one goes left to right and the other one goes right to left.
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OK?
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So it depends on how you read it.
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Or you can simply just use the algebraic way and take your two y values, subtract them,
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and then take your two x values and subtract them.
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Cool.
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So that's how you find the rate of change from a graph.
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And our rate of change from doing the graph is what we call the slope.