Question

latoya is riding her bike. the distance she travels varies directly with the number of revolutions (turns) her wheels make. see the graph below.

distance
traveled
(feet)

number of revolutions

(a) how many revolutions does latoya make per foot of
distance traveled?

revolution(s)

(b) what is the slope of the graph?

Explanation:

Part (a)

Step1: Identify two points on the graph

From the graph, when \( x = 2 \) (revolutions), \( y = 10 \) (feet). We need revolutions per foot, so we calculate \( \frac{\text{revolutions}}{\text{distance}}=\frac{2}{10} \).

Step2: Simplify the fraction

\( \frac{2}{10}=\frac{1}{5} = 0.2 \)

Step1: Recall the slope formula

The slope \( m \) of a line is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \( (0,0) \) and \( (2,10) \) (from the graph).

Step2: Calculate the slope

\( m=\frac{10 - 0}{2 - 0}=\frac{10}{2}=5 \)

Answer:

\( 0.2 \) (or \( \frac{1}{5} \))

Part (b)