The 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 35 minutes of calls is $15.10, and the remaining credit after 73 minutes of calls is $9.78. What is the remaining credit after 94 minutes of calls?

Answer: the remaining credit after 94 minutes of calls is $6.84

Step-by-step explanation:

let x represent the total calling time made with the card.

Let y represent the remaining amount of credit on the card

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (9.78 - 15.1) / (73 - 35)

m = - 5.32/38 = - 0.14

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 35, y = 15.1 and m = - 0.14 into y = mx + c. It becomes

15.1 = - 0.14 * 35 + c

15.1 = - 4.9 + c

c = 15.1 + 4.9

c = 20

The linear function becomes

y = - 0.14x + 20

The remaining credit after 94 minutes of calls would be

y = - 0.14 * 94 + 20

y = - 13.16 + 20

y = $6.84