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), as shown in the figure below. The remaining credit after 45 minutes of calls is $22.80 , and the remaining credit after 64 minutes of calls is $19.76 . What is the remaining credit after 73 minutes of calls?

Answer 1

The remaining credit after 73 minutes of calls is $1.73

Step-by-step explanation:

To solve this problem, we can use the information given to find the equation of the linear function. We are given two points on the graph: (45, $22.80) and (64, $19.76). Using these points, we can find the slope of the line as follows:

Slope, m = (change in y)/(change in x) = ($19.76 - $22.80)/(64 - 45) = -$0.3067 per minute

Now that we know the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (45, $22.80), we can plug in the values to find the equation:

y - $22.80 = -$0.3067(x - 45)

Simplifying the equation gives:

y = -$0.3067x + $23.2585

Now we can substitute x = 73 into the equation to find the remaining credit after 73 minutes of calls:

y = -$0.3067(73) + $23.2585

y = $1.7311