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 28 minutes of calls is $26.64, and the remaining credit after 62 minutes of calls is $22.56. what is the remaining credit after 89 minutes of calls?

Explanation:

Step1: Find the slope of the linear - function

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the calling time in minutes and $y$ be the remaining credit in dollars. We have the points $(28,26.64)$ and $(62,22.56)$.
$m=\frac{22.56 - 26.64}{62 - 28}=\frac{-4.08}{34}=-0.12$

Step2: Find the y - intercept of the linear function

Use the point - slope form of a line $y - y_1=m(x - x_1)$ and then convert it to the slope - intercept form $y=mx + b$. Let's use the point $(28,26.64)$ and $m=-0.12$.
$y-26.64=-0.12(x - 28)$
$y-26.64=-0.12x+3.36$
$y=-0.12x + 30$

Step3: Find the remaining credit after 89 minutes

Substitute $x = 89$ into the equation $y=-0.12x + 30$.
$y=-0.12\times89+30$
$y=-10.68 + 30$
$y = 19.32$

Answer:

$19.32$