In the graph shown above, what is the x-coordinate of point n if the slope of the line mn is ⅓?


First, let’s get an idea of which answer choices are out of the ballpark. We are looking for the x-coordinate of point n. Well, before we start using complicated formulas, let’s do a little measuring. The x-coordinate for point m is 3. This means that the horizontal distance from 0 to m is 3. Mark off this distance on your scratch paper. Now, try measuring the horizontal distance between 0 and point n. Did you get about 6? That’s what we got. Because these figures are drawn only roughly to scale, we can’t guarantee that the answer is going to be exactly 6, but it ought to be close to 6 anyway. So which answer choices can we get rid of? Choices (A), (C), and (D) are all out of the ballpark. The only possible answer this time is (B).

If you needed to get this one the traditional way, you would have to use the slope formula backward.

\(\text { Slope }=\frac{\text { change in } y}{\text { change in } x} \Leftrightarrow \frac{1}{3}=\frac{2-1}{x-3}\)

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