y=mx+b find a equation

Question

The phone company Fee & Fee has a monthly plan where a customer pays a flat monthly fee, and then a set rate per minute. If a customer uses 350 minutes, the monthly cost will be $75. If the customer uses 540 minutes, the monthly cost will be $94.

Find the equation of the plan in the form  where  is the number of monthly minutes used and  is the total monthly cost of the Fee & Fee plan.

Answer 1

For this problem, we're going to have to think of these two pieces of data as points on a graph. Let's suppose that your x axis determines the amount of minutes the customer has used and the y axis determines the cost after having used x amount of minutes.

Now, our points are (350, 75) and (540, 94) so we can use these to find the slope of our line.

We'll use the formula m = (y2 - y1) / (x2 - x1) which gives us (94 - 75) / (540 - 350) = 19/190 = 1/10.

So our slope is 1/10.

Now that we know our slope, we want to use either of our 2 points along with the slope we just found in order to find the equation of our line.

For this, we'll use the point-slope formula: y - y1 = m(x - x1)

We'll use the point (350, 75) so we get: y - 75 = 1/10 (x - 350)

Now, we solve for y to get: y = 1/10x + 40

This means that the flat monthly fee (regardless of how many minutes have been used) is $40.