What is the remaining credit after 81 minutes of calls?

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 43 minutes of calls is $14.84

and the remaining credit after 69 minutes of calls is $11.72

What is the remaining credit after 81 minutes of calls?

Answer 1

Hi Isabelle,

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 43 minutes of calls is $14.84

and the remaining credit after 69 minutes of calls is $11.72

What is the remaining credit after 81 minutes of calls?

GIVEN:

1) Linear Function (Linear equation .. this means it's the equation of a line. The x axis is total calling time, the y axis is credit remaining in hours)

2) remaining credit after 43 minutes of calls is $14.84 This is a point on your graph (43min, $14.84)

3) and the remaining credit after 69 minutes of calls is $11.72. This is a point on your graph (69min, $11.72)

FIND What is the remaining credit after 81 minutes of calls?

So. They are giving you information about 2 data points on a line

From the two data points you can write the equation of the line.

Using the equation of the line you can put the value 81 in for x and determine what y is in $

1) Find the equation of a line given 2 data points.

(43min, $14.84) (69min, $11.72)

(y-y1) = m(x-x1) This is the point slope form of a line where m is the slope of the line.

m = (y2-y1)/ (x2-x1). m = (11.72 - 14.84) / (69-43) = (-3.12/26) = -0.12

so m=-0.12

now use a point to determine the equation of the line

(y-14.84) = (-0.12) (x - 43)

y -14.84 = -0.12x + 5.16

y = -0.12x + 20

2) Now use the equation from above to determine the cost when x = 81 min

y= -0.12 (81) + 20

y = 10.28

So you will have $10.28 Credit left.

Hope this helps

Let me know if you have any questions !