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 39 minutes of calls is $25.32, and the remaining credit after 57 minutes of calls is $23.16. What is the remaining credit after 60 minutes of calls?

Answer 1

One way to write a linear equation is the formula y = mx + b where m is the slope of the function and b is the y-intercept. For this reason, it is known as slope-intercept form.

The slope os calculated via the formula $\frac{y_2 - y_1}{x_2 - x_1}$. Lets calculate the slope of the equation first.

$\frac{23.16 - 25.32}{57 -39}$

$\frac{-2.16}{18}$

$-0.12$

So the slope is -0.12. This means for every minute of time used, $0.12 of credit is used. Next, lets plug in the value for m, and the values of an x and y point to find b.

y = 0.12x + b

23.16 = -0.12(57) + b

23.16 = -6.84 + b

30 = b

So, our final equation is y = -0.12x + 30.

Finally, we can use this equation to find the answer to the last part by plugging the value into x.

y = -0.12(60) + 30

y = -7.2 + 30

y = 22.8

So when 60 minutes have been used, there will be $22.80 worth of credit left.

Answer 2

The remaining credit after 60 minutes of calls is required.

The remaining credit after 60 minutes of calls is $22.80.

After 39 minutes

Remaining credit is $25.32

After 57 minutes

Remaining credit is $23.16

Let us take the minutes as $x$ and remaining credit as $y$ the points will be

$(39,25.32)$

$(57,23.16)$

Since, it is a linear function the equation will be

$y-25.32=\dfrac{23.16-25.32}{57-39}(x-39)\\\Rightarrow y-25.32=-0.12(x-39)\\\Rightarrow y-25.32=-0.12x+4.68\\\Rightarrow y=-0.12x+4.68+25.32\\\Rightarrow y=-0.12x+30$

For 60 minutes $x=60$

$y=-0.12\times 60+30=22.8$

The remaining credit after 60 minutes of calls is $22.80.

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