ShmoopTube

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And here's your shmoop du jour...

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What is the equation of the line shown in the graph below?

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And here are the potential answers…

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So… what is this question asking?

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Can we, like Superman, just look at a graph and come up with the equation?

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Sure we can. Unless slope-intercept form is our Kryptonite…

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Well, we know the y equals mx plus b format, and that approach should fit easily here,

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since we need 2 things to make a linear equation – the slope and a point at which it intersects.

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Just by looking at the line we know the slope is positive,

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because it moves in an upward direction from left to right.

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Since we know slope is rise over run, we can just figure this thing out.

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Note that if we go forward 3 hops from the x intercept to the origin and then look straight up…

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we see 4 hops above us.

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So we rise 4 units for every 3 we run and that gives us a slope of 4 thirds.

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Now we plug in the y intercept, which is here at 0, 4 –

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i.e. where the line crosses the y axis.

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That positive 4 is our “b.”

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And if we glance at the answers, we can see ‘em right here… it’s gotta be A because

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C and D have the wrong slope and intercept, and B has the wrong slope sign.

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A it is. As in, "Action hero."

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