Question

The given graph shows the relationship between the fee charged by a cleaning company (in $\$$) and the time (in hours). Calculate the fee charged by the company per hour based on the given information.

• A. $\$75$ per h
• B. $\$30$ per h
• C. $\$60$ per h
• D. $\$50$ per h

Answer 1

The correct option is D $\$50$ per h

Let’s consider two points on the graph, $(1,50)$ and $(0,0)$.
We can write, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(1,50)$.
Here, the fee charged per hour can be calculated by finding the slope of the graph.
Fee charged per hour = slope= $=\frac{\text{rise}}{\text{run}}=\frac{\text{change in}y}{\text{change in}x}=\frac{y_2-y_1}{x_2-x_1}=\frac{50-0}{1-0}=\frac{50}{1}\$50$ per h

Alternate solution:
On a graph of a proportional relationship, point $(1,k)$ represents the unit rate $k:1$, and the constant of proportionality, $k$.
So, from the point $(1,50)$, the unit rate which is the fee charged per hour is determined as $\$50$ per h.