ShmoopTube

00:04

Function Rules, Tables, and Graphs, a la Shmoop.

00:11

Jack and Jill went up the hill to fetch a pail of water...

00:14

...because they’d entered a habanero-eating contest.

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Too bad the troll will only let them drink if they find and graph the function of the hill’s incline.

00:24

The troll provides a table of points on the hill.

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(0,3), (-1,1), and (1,5)

00:32

Jack and Jill seem a little preoccupied, so let’s give them a hand before they really

00:36

burn their mouths.

00:38

First, let's draw our coordinate axes, x and y.

00:41

We can plot the points on a graph..and when we connect the dots, we can see that a line emerges.

00:48

To find the function rule of the line, we can use the slope intercept form of a line:

00:54

y equals mx plus b.

00:57

To calculate m, the slope, we need to find the rise and run between two points on the line.

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So let’s use (0,3) and (1,5).

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Slope equals rise…

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...the distance between the y-points…

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...over run...

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…the distance between the two x-points.

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When we plug in our two points, we get 5 minus three, over 1 minus 0.

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Or 2 over 1.

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Also known as 2.

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Now our equation is y equals 2x plus b.

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b represents the y-intercept, or the y-value when x equals 0.

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The troll gave us this point.

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The y-intercept is 3.

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Which makes our equation y equals 2x plus 3.

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Open sesame!

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Now Jack and Jill can go find water at the bottom of the well.

02:00

Thanks, Troll.

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