Answer
See below:
Work Step by Step
Since the telephone billing plan is $\$50$ per month that buys 400 minutes and the additional time costs $\$0.3$ per minute.
So, we will write the piecewise model function for the telephone billing plan as follows:
$C\left( t \right)=\left\{ \begin{align}
& 50\text{ if 0}\le t\le 4\text{00} \\
& \text{50+0}\text{.3}\left( t-400 \right)\text{ if }t>400 \\
\end{align} \right.$
Solve the expression $\text{50+0}\text{.3}\left( t-400 \right)$ and write the expression in the simplified form as below:
$\begin{align}
& \text{50+0}\text{.3}\left( t-400 \right)=50+0.3t-0.3\times 400 \\
& =50+0.3t-120 \\
& =0.3t-70
\end{align}$
Thus, the simplified form of the expression for the telephone billing plan is as below:
$C\left( t \right)=\left\{ \begin{align}
& 50\text{ if 0}\le t\le 4\text{00} \\
& 0.3t-70\text{ if }t>400 \\
\end{align} \right.$
The function shown above consists of 2 straight lines.
So the function can be written as $y=50$ for $0\le t\le 400$ and $y=0.3t-70$ for $t>400$
Now the line $y=50$ is a line parallel to the x axis and at a distance 50 units above the x axis.
The line $y=0.3t-70$ is a line with slope 0.3 and y intercept $-70$.
