Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes).

Question

Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.14. There is $34.06 in credit remaining on the card after 29 minutes of calls. How much credit will there be after 15 minutes of calls?

Answer 1

Need to find the equation of the linear function representing the relationship:

y = mx + b

where m is slope and b is y-intercept:

we are given slope is -0.14

y = -0.14x + b

we also know that:

when x = 29, y = 34.06

substituting those values into the equation we can find b:

34.06 = -0.14(29) + b

34.06 = -4.06 + b

38.12 = b

y = -0.14x + 38.12

now we are given x = 15 and we need to find y:"

y = -0.14(15) + 38.12

y = 36.02