Question

keith is riding his bike. the distance he travels varies directly with the number of revolutions (turns) his wheels make. see the graph below. (a) how many revolutions does keith make per foot of distance traveled? revolution(s) (b) what is the slope of the graph?

Explanation:

Step1: Find the unit rate for part (a)

From the graph, when \(x = 2\) (revolutions), \(y=8\) (feet). The number of revolutions per foot is \(\frac{x}{y}\). Substitute \(x = 2\) and \(y = 8\): \(\frac{2}{8}=\frac{1}{4}\)

Step2: Find the slope for part (b)

The slope \(m\) of a line \(y=mx\) (direct - variation \(y = kx\)) is given by \(m=\frac{y}{x}\). Using the point \((2,8)\), \(m=\frac{8}{2}=4\)

Answer:

(a) \(\frac{1}{4}\)
(b) \(4\)