Answer
$$ C(x)= \left\{ \begin{array}{2} \$35 & \quad \$0 \leq x \leq \$400 \\ \$0.10x - \$5 &\quad \$400 \lt x \leq \$600 \end{array} \right. $$
Work Step by Step
The problem states that the first $400 \ minutes$ on the cell phone plan are free, so we can express this with an equation $y=\$35$ for domain $[0,400]$. After 400 minutes, each additional minute is $\$0.10$. So, the slope of our equation is $0.1$. We now need to find the y-intercept, so we can write our equation as $y=0.1(x-400)+35$. Solving this equation out gives us $y=0.1x-5$ for the domain $(400,600]$.
