Question

Joseph’s cell phone service charges him $\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{15}$ per each text message sent. Write an equation that represents the cost $\mathit{C}$of his cell phone service for the text message $\mathit{t}$sent each month.

Short answer

The required equation is $\mathit{C}\mathbf{=}\mathbf{0}\mathbf{.15}\mathit{t}$.

Step-by-step solution

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:

$C=mt+b$

Here $C$is the cost of Joseph’s cell phone service and $t$is number of text message sent.

Step 3. Find the equation.

Joseph’s cell phone service charges $\$0.15$per each text message.

Therefore, $m=0.15$.

There is no additional charge mentioned. Hence the $y$-intercept is 0.

That is, $b=0$.

Substitute $m=0.15$and $b=0$in $C=mt+b$to get the required equation.

$\begin{array}{c}C=mt+b\\ C=0.15t+0\\ C=0.15t\end{array}$

Hence the required equation is $C=0.15t$.