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We're asked to graph the proportional relationship shown in the table below.
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And they give us a table of x values and the corresponding y values.
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So we see when x is equal to 0, y is equal to 0.
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Then they give us a bunch of other points.
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When x is 3, y is 0.5.
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When x is 6, y is 1.
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So on and so forth.
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So let's graph one of these that actually have integer values for both coordinates.
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So when x is 6, y is 1.
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So we only need 2 points to specify the line.
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So we've actually graphed it.
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But then they also ask us, "What is the slope of this line?"
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And we just have to remind ourselves:
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Our slope is our change in y for a given change in x.
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So, for example – Or another way to think about it:
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What is your change in y over your change in x?
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So here, our x changed by 6.
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It went from 0 to 6.
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And our y changed by 1.
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So our change in y over our change in x,
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(which is the definition of slope),
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our change in y is 1 when our change in x is 6.
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We see that right over here.
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Our change in y is 1 when our change in x is 6.
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Let's check our answer.
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We got it right.