Question

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

Explanation:

Step1: Recall the formula for slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a direct - variation graph \(y = mx\) (where \(y\) is the number of revolutions and \(x\) is the distance traveled), the slope \(m\) represents the number of revolutions per foot.

Step2: Choose two points on the line

Let's choose the points \((0,0)\) and \((80,8)\) (we can also choose other non - zero points).

Step3: Calculate the slope

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \(x_1 = 0,y_1 = 0,x_2=80,y_2 = 8\). Then \(m=\frac{8 - 0}{80 - 0}=\frac{8}{80}=\frac{1}{10}\)

Answer:

(a) \(\frac{1}{10}\)
(b) \(\frac{1}{10}\)