Q13. - Algebra 1

Question

A rental company charges $\mathbf{\backslash (}\mathbf{9}\mathbf{.}\mathbf{50}$ per hour for a scooter plus a $\mathbf{\backslash )}\mathbf{15}$ fee. Write the equation in Slope-intercept form for the total rental cost $\mathit{C}$ of renting a scooter for $\mathit{h}$ hours.

Step-by-Step Solution

Answer

The slope-intercept form for the total rental cost $C$ of renting a scooter for h hours is: $\mathit{C}\mathbf{=}\mathbf{9}\mathbf{.50}\mathit{h}\mathbf{+}\mathbf{15}$

Step 1. State the concept of ‘Slope-intercept form’.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the$y$-intercept (the$y$-coordinate of the point where the line intersects the$y$-axis).

Step 2. Write the general algebraic expression of slope-intercept form.

The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the$y$-axis.

Consider a straight line of slope$\text{'}m\text{'}$and$y$-intercept$\text{'}b\text{'}$.The slope intercept form equation for a straight line with a slope,$\text{'}m\text{'}$, and$\text{'}b\text{'}$as the$y$-intercept can be given as:  

$C=mh+b$.

Where$C$is the total rental cost and h is the time in hours.

Step 3. Find the equation.

The rental company charges $\$9.50$ per hour for a scooter.

This rate of change is the slope of the required equation.

Hence, $m=9.50$

Also the company charges extra $\$15$ as a fee.

This extra fee is the $y$-intercept of the required equation.

Hence, $b=15$

Substitute $m=9.50$ and $b=15$ in $C=mh+b$ to get the required equation.

$\begin{array}{c}C=mx+b\\ C=9.50h+15\end{array}$

Hence the required equation.