Q5. - Algebra 1

Question

Write an equation in slope-intercept form for the total rental cost $C$ for a pontoon boat used for t  hours.

Step-by-Step Solution

Answer

The equation for total rental cost $C$ for the pontoon used for t hours is $\mathit{C}\mathbf{=}\mathbf{60}\mathit{t}\mathbf{+}\mathbf{20}$.

Step 1. State the concept of a straight line.

The standard form of slope and intercept form of the straight line is $y=mx+c$.

Here, $m$ is the slope of the straight line and $c$ is the $y$-intercept of the equation.

The cleaning fee is the intercept of the line on the $y$-axis while the pontoon boat rental is the slope of the equation.

Step 2. Substitute the values from the given information.

Substitute, the value of the slope, $m=60$ and the $y$-intercept is $c=20$.

Write the equation in the slope-intercept form. 

$\begin{array}{l}y=mx+c\\ y=60x+20\end{array}$

Step 3. Replace the variables to get slope-intercept form.

Replace $y$ with $C$ and $x$ with $t$ as $C$ is the dependent variable and $t$ is the independent variable.

$\begin{array}{l}y=C,\\ x=t\\ y=60x+20\\ C=60t+20\end{array}$

The equation of the straight line in the slope and intercept form is $C=60t+20$, where $t$ is the number of hours.