19. COMMUNICATIONS A telephone company charges \( \$ 4.95 \) per month for long distance calls plus \( \$ 0.05 \) per minute. The monthly cost \( c \) of long distance calls can be described by the equation \( c=0.05 m+4.95 \), where \( m \) is the number of minutes. a. Find the \( y \)-intercept of the graph of the equation. b. Graph the equation. c. If you talk 140 minutes, what is the monthly cost?

To solve the problem, let's break it down step by step. ### a. Find the \( y \)-intercept of the graph of the equation. The equation given is: \[ c = 0.05m + 4.95 \] To find the \( y \)-intercept, we set \( m = 0 \) (which represents 0 minutes of calls) and solve for \( c \): \[ c = 0.05(0) + 4.95 = 4.95 \] Thus, the \( y \)-intercept is \( (0, 4.95) \). ### b. Graph the equation. To graph the equation \( c = 0.05m + 4.95 \): 1. **Plot the \( y \)-intercept**: Start by plotting the point \( (0, 4.95) \). 2. **Find another point**: Choose a value for \( m \) to find another point. For example, let’s use \( m = 100 \): \[ c = 0.05(100) + 4.95 = 5 + 4.95 = 9.95 \] So, the point \( (100, 9.95) \) can be plotted. 3. **Draw the line**: Connect the points \( (0, 4.95) \) and \( (100, 9.95) \) with a straight line. The slope of the line is \( 0.05 \), indicating that for every additional minute, the cost increases by \( \$0.05 \). ### c. If you talk 140 minutes, what is the monthly cost? To find the monthly cost for \( m = 140 \): \[ c = 0.05(140) + 4.95 \] Calculating this: \[ c = 7 + 4.95 = 11.95 \] Thus, if you talk for 140 minutes, the monthly cost is \( \$11.95 \). ### Summary of Results: - **\( y \)-intercept**: \( (0, 4.95) \) - **Monthly cost for 140 minutes**: \( \$11.95 \)