Question

Suppose that the monthly cost of a long-distance phone plan (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of 0.11. See the figure below.
The monthly cost for 30 minutes of calls is $18.64. What is the monthly cost for 38 minutes of calls?

Answer 1

To find the monthly cost for 38 minutes of calls based on the linear relationship, we can use the information given about the cost for 30 minutes and the slope of the line.

1. **Identify the slope and the known point:**
- The slope (m) is 0.11.
- The cost for 30 minutes (x = 30) is $18.64 (y = 18.64).

2. **Use the point-slope formula for a linear function:**
The formula is \( y - y_1 = m(x - x_1) \), where:
- \( (x_1, y_1) \) is the known point (30, 18.64),
- \( m \) is the slope (0.11),
- \( x \) is the new calling time (38 minutes),
- \( y \) is the monthly cost for that calling time.

3. **Substituting the values into the equation:**
\[
y - 18.64 = 0.11(38 - 30)
\]

4. **Calculating the right side:**
\[
y - 18.64 = 0.11 \times 8
\]
\[
y - 18.64 = 0.88
\]

5. **Solving for y:**
\[
y = 18.64 + 0.88
\]
\[
y = 19.52
\]

Therefore, the monthly cost for 38 minutes of calls is **$19.52**.