Question

The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone.

Answer 1

The equation of a line in slope-intercept form is:

$y=mx+b$

Where m is the slope of the line and b is the y-intercept.

Also, in this problem, x is the number of monthly minutes used and y is the total monthly payment of the Splint plan.

The slope can be found by the following formula:

$m=\frac{y2-y1}{x2-x1}$

Where (x1,y1) and (x2,y2) is the given information, x1=280 min, y1=$178, x2=730 min and y2=$403.

Replace these values and solve for m:

$\begin{gathered} m=\frac{403-178}{730-280}=\frac{225}{450} \\ \text{Simplify} \\ m=\frac{1}{2} \end{gathered}$

Now, replace m and one of the coordinates in the equation of the line and solve for b:

$\begin{gathered} 178=\frac{1}{2}280+b \\ 178=140+b \\ b=178-140 \\ b=38 \end{gathered}$

Thus, the equation is:

$y=\frac{1}{2}x+38$

b. The monthly cost, if 910 minutes are used, is:

$\begin{gathered} y=\frac{1}{2}910+38 \\ y=455+38 \\ y=493 \end{gathered}$

If 910 minutes are used, the total cost will be 493 dollars.