Can someone please help me?! I keep trying to solve it but I keep getting the wrong answer

Question

I've been trying to solve this math problem for over 45 minutes. I had this math problem last week and I skipped it. I asked on here but no one answered. I thought that if I came back to it I'd have a better understanding but I'm still just as stuck. Here's the problem:

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 29 minutes of calls is $26.23, and the remaining credit after 55 minutes of calls is $22.85. What is the remaining credit after 59 minutes of calls?

Answer 1

Let x be the number of minutes used and y be credit remained.

Since the credit remaining on a phone card is a linear function then we need to find this linear function. To find this, we first need to find the slope.

We are given (29,26.23) and (55,22.85).

Slope = (22.85-26.23)/(55-29) = -3.38/26 = -1.69/13 = -0.13

Hence the linear equation will be

y - 22.85 = -0.13 (x-55)

y = -0.13x +30

Thus when x is 59 minutes we see that y = -0.13(59) +30 = -7.67+30 = 22.33

Answer 2

after 29 minutes $26.23 left

after 55 $22.85 left

after 59 minutes, how much is left?

55-29 = 26 minutes costing 26.23-22.85 = $3. 38

or $3.38/26 = 13 cents per minute

for another 4 minutes, from 55 to 59 minutes, it used up 4(3.38/26) = 2(3.38/13) = $0.26 = 26 cents

deduct that from $22.85

22.85-.26 = $22.59 left