Question

the phone company a fee and fee 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 360 minutes, the monthly cost will be \\$146. if the customer uses 940 minutes, the monthly cost will be \\$349.

a) find an equation in the form (y = mx + b), where (x) is the number of monthly minutes used and (y) is the total monthly of the a fee and fee plan.

answer: (y = \\)

do not use any commas in your answer.

b) use your equation to find the total monthly cost if 613 minutes are used.

answer: if 613 minutes are used, the total cost will be dollars.

Explanation:

⚡ Using what you learned: Creating Equations to Model Relationships

Step 1: Identify the data points

Let \( x \) represent the number of monthly minutes used, and \( y \) represent the total monthly cost.

From the problem, we have two data points in the form \((x, y)\):

$$ (x_1, y_1) = (360, 146) $$

$$ (x_2, y_2) = (940, 349) $$

Step 2: Find the slope \( m \)

The slope \( m \) represents the cost per minute:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

$$ m = \frac{349 - 146}{940 - 360} $$

$$ m = \frac{203}{580} $$

$$ m = 0.35 $$

Step 3: Find the y-intercept \( b \)

Using the slope-intercept form \( y = mx + b \) with the point \((360, 146)\):

$$ 146 = 0.35(360) + b $$

$$ 146 = 126 + b $$

$$ b = 20 $$

Thus, the equation is:

$$ y = 0.35x + 20 $$

Step 4: Calculate the cost for 613 minutes

Substitute \( x = 613 \) into the equation:

$$ y = 0.35(613) + 20 $$

$$ y = 214.55 + 20 $$

$$ y = 234.55 $$

Answer:

A) \( y = 0.35x + 20 \)

B) \( 234.55 \)