A telephone company offers a monthly cellular phone plan for $\mathrm{\$}25.00$. It includes 350 free minutes plus $\mathrm{\$}0.20$ per minute for additional minutes. The following function gives the monthly cost for a subscriber, where $\mathrm{x}$ is the number of minutes used. Simplify the expression in the second line of the piecewise function. Then use point-plotting to graph the function
$$C(x)=\{\begin{array}{ll}25.00& \text{ if }0\le x\le 350\\ 25.00+0.20(x-350)& \text{ if }x>350\end{array}$$

Step 1 ：The first step is to simplify the expression in the second line of the piecewise function. This involves distributing the 0.20 to both terms inside the parentheses, resulting in the simplified expression $0.20x-45.00$.

Step 2 ：Next, we need to plot the function. Since it's a piecewise function, we'll plot two separate lines: one for $0\le x\le 350$ and another for $x>350$.

Step 3 ：For the range $0\le x\le 350$, the cost is a constant $25.00, represented by a horizontal line on the graph.

Step 4 ：For the range $x>350$, the cost increases linearly according to the simplified expression $0.20x-45.00$. This is represented by a line with a slope of 0.20 and a y-intercept of -45.00 on the graph.

Step 5 ：$\boxed{{\displaystyle \text{Final Answer: The simplified expression for the second line of the piecewise function is }0.20x-45.00.\text{The graph of the function shows a constant cost of }\$25.00\text{ for }0\le x\le 350\text{ and a linear increase in cost for }x>350.\text{The slope of the line for }x>350\text{ is }0.20,\text{ which represents the cost per additional minute. The y-intercept of this line is }-45.00,\text{ which is the result of the simplification of the expression }25.00+0.20(x-350).}}$