Question

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

Explanation:

Step1: Find the relationship between distance and revolutions

Since the distance \(y\) varies directly with the number of revolutions \(x\), the equation is \(y = kx\), where \(k\) is the constant of proportionality (slope). From the graph, when \(x = 4\), \(y = 20\).

Step2: Calculate the slope (\(k\))

Using the formula \(k=\frac{y}{x}\), substitute \(x = 4\) and \(y = 20\). So \(k=\frac{20}{4}=5\). The slope of the graph (which represents distance per revolution) is \(5\).

Step3: Calculate revolutions per foot

Revolutions per foot is the reciprocal of distance per revolution. So it is \(\frac{1}{k}\). Since \(k = 5\), revolutions per foot is \(\frac{1}{5}=0.2\)

Answer:

(a) \(0.2\) revolution(s)
(b) \(5\)