Question

The phone company NextFell 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. If a customer uses 490 minutes, the monthly cost will be $254.5. If the customer uses 820 minutes, the monthly cost will be $403.

A) Find an equation in the form
y
=
m
x
+
b
,
where
x
is the number of monthly minutes used and
y
is the total monthly cost of the NextFell plan.

Answer 1

Answer: Let's assume:

x = number of monthly minutes used

y = total monthly cost of the NextFell plan

We are given two data points:

When x = 490 minutes, y = $254.5

When x = 820 minutes, y = $403

We can use these two points to find the equation of the line in the form y = mx + b.

Step 1: Find the slope (m) of the line.

The slope (m) of the line can be calculated using the formula:

m = (change in y) / (change in x)

m = (403 - 254.5) / (820 - 490)

m = 148.5 / 330

m = 0.45

Step 2: Find the y-intercept (b) of the line.

To find the y-intercept (b), we can use one of the data points and substitute the values of x, y, and m.

Using the first data point (x = 490 minutes, y = $254.5):

254.5 = 0.45 * 490 + b

254.5 = 220.5 + b

Now, solve for b:

b = 254.5 - 220.5

b = 34

Step 3: Write the equation of the line.

Now that we have the slope (m = 0.45) and the y-intercept (b = 34), we can write the equation of the line:

y = 0.45x + 34

This equation represents the total monthly cost (y) of the NextFell plan based on the number of monthly minutes used (x).