Question

The given graph represents the total fees charged by a bike rental shop. What will the rent of one bike and registration fees be based on the graph?

• A. Rent of one bike $=\$10$, registration fees $=\$10$
• B. Rent of one bike $=\$15$, registration fees $=\$5$
• C. Rent of one bike $=\$10$, registration fees $=\$5$
• D. Rent of one bike $=\$15$, registration fees $=\$15$

Answer 1

The correct option is C Rent of one bike $=\$10$, registration fees $=\$5$

Points on the given graph can be represented in the form of a table.

$\text{Number of bikes}$	$\text{Total rent (\$)}$
1	15
2	25
3	35

$\text{Slope}=\frac{\text{change in y coordinate}}{\text{change in x coordinate}}=\frac{\text{change in total rent}}{\text{change in number of bikes}}=\frac{25-15}{2-1}=10$
$y$-intercept $=5$

Equation of the function: $y=10x+5$

Therefore, the total rent for 1 bike $=(10\times 1)+5=\$15$
But this is the total rent. To find the rent for one bike, we will have to subtract the registration fee.

To find the registration fee, we need to find the total rent when no bike is rented.
Registration fee $=(10\times 0)+5=\$5$

Therefore, rent of one bike $=15-5=\$10$