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=(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=(403-178)/(730-280)=(225)/(450) \\ \text{Simplify} \\ m=(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=(1)/(2)280+b \\ 178=140+b \\ b=178-140 \\ b=38 \end{gathered}`

Thus, the equation is:

`y=(1)/(2)x+38`

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

`\begin{gathered} y=(1)/(2)910+38 \\ y=455+38 \\ y=493 \end{gathered}`

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