Question

The credit remaining on a phone card (In dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 42

minutes of calls is $13.70, and the remaining credit after 59 minutes of calls is $11.15. What is the remaining credit after 65 minutes of calls?

Answer 1

The remaining credit after 65 minutes of calls is $10.25.

Step-by-step explanation:

To find the remaining credit after 65 minutes of calls, we need to determine the equation of the linear function that relates the credit remaining to the total calling time. Let's call the remaining credit C and the calling time T. We are given two points on the line: (42, 13.70) and (59, 11.15). We can use the point-slope form of a linear equation to find the equation of the line.

First, calculate the slope using the formula: slope = (C2 - C1) / (T2 - T1). Substituting the values, we get: slope = (11.15 - 13.70) / (59 - 42) = -2.55 / 17 = -0.15.

Next, use the point-slope form: C - C1 = m(T - T1), where m is the slope and (T1, C1) is one of the points. Let's use the point (42, 13.70): C - 13.70 = -0.15(T - 42).

Now, substitute T = 65 and solve for C: C - 13.70 = -0.15(65 - 42). C - 13.70 = -0.15(23). C - 13.70 = -3.45. C = -3.45 + 13.70 = 10.25.

The remaining credit after 65 minutes of calls is $10.25.