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. if a customer uses 370 minutes, the monthly cost will be $193.5. if the customer uses 750 minutes, the monthly cost will be $364.5.

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 splint plan.
answer: y = _______
b) use your equation to find the total monthly cost if 625 minutes are used.
answer: if 625 minutes are used, the total cost will be ______ dollars.

Answer 1

To find the equation representing the monthly cost of the Splint plan, we use the slope-intercept form of a linear equation. The equation is y = 0.49x + 16.15. When 625 minutes are used, the total monthly cost will be $322.4.

Step-by-step explanation:

To find the equation representing the monthly cost of the Splint plan, we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, y represents the total monthly cost and x represents the number of monthly minutes used. To find the equation, we need to determine the values of m (slope) and b (y-intercept).

We are given two data points: (370 minutes, $193.5) and (750 minutes, $364.5).

Using the slope formula, we can find the slope:

1. Let x1 = 370, y1 = 193.5, x2 = 750, and y2 = 364.5
2. Slope (m) = (y2 - y1) / (x2 - x1) = (364.5 - 193.5) / (750 - 370) = 0.49

Now, let's substitute one of the data points (370 minutes, $193.5) into the equation:

1. x = 370 and y = 193.5
2. 193.5 = 0.49 * 370 + b
3. b = 193.5 - 0.49 * 370 = 16.15

Therefore, the equation representing the monthly cost of the Splint plan is y = 0.49x + 16.15.

To find the total monthly cost when 625 minutes are used, we can substitute x = 625 into the equation:

1. x = 625
2. y = 0.49 * 625 + 16.15
3. y = 306.25 + 16.15 = $322.4 (rounding to the nearest cent)

So, if 625 minutes are used, the total cost will be $322.4.