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?

Short 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 $6hours$is $40\$$.

Step-by-step solution

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 $\$40$.