Q16. - Algebra 1

Question

A sporting goods company near the beach rents bicycles for $\backslash (10$ plus $\backslash )5$ per hour. Write an equation in slope-intercept form that shows the total cost, $y$ of renting a bicycle for $x$ hours. How much would it cost Emily to rent a bicycle for $6$ hours?

Step-by-Step Solution

Answer

The equation in slope-intercept form that shows the total cost, $y$, of renting a bicycle for hours is  $\mathit{y}\mathbf{=}\mathbf{5}\mathit{x}\mathbf{+}\mathbf{10}$.

The cost to rent a bicycle for $6 hours$ is $40\$$.

Step1. Given

It is given that a sporting goods company near the beach rents bicycles for $\$10$ plus $\$5/hr$ 

Step2. Formula used

The equation of the line in slope-intercept is given by $y=mx+c$, where $m$ is the slope of the line and $c$  is the $y$-intercept.

Let $x$ be the number of hours the cycle is rented and $y$ be the total cost.

Therefore,

$\begin{array}{c}y=5\times x+10\\ y=5x+10\end{array}$

Therefore, the equation in slope-intercept form that shows the total cost, $y$, of renting a bicycle for $x$  hours is $y=5x+10$.

Step 3. Calculation

The equation in slope-intercept form that shows the total cost, $y$, of renting a bicycle for $x$ hours is  $y=5x+10$.

It is given that the bicycle is rented for 6 hours. Therefore, the value $x$ is 6.

Substitute 6 for $x$ in $y=5x+10$.

$\begin{array}{c}y=5x+10\\ =5\left(6\right)+10\\ =30+10\\ =40\end{array}$

Therefore, the cost to rent a bicycle for 6 hours is $\$40$.