Question

tony 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 tony make per foot of distance traveled?
revolution(s)
(b) what is the slope of the graph?

Explanation:

Step1: Pick point for direct variation

From the graph, take the point $(x=4, y=12)$ where $x$ = revolutions, $y$ = distance.

Step2: Find revolutions per foot

Calculate ratio $\frac{x}{y}$:
$\frac{4}{12} = \frac{1}{3}$

Step3: Calculate slope of the graph

Slope is $\frac{\Delta y}{\Delta x}$, use the same point:
$\frac{12}{4} = 3$

Answer:

(a) $\frac{1}{3}$
(b) $3$