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Let's break down the problem step by step to solve it.

### A) Finding the Equation:
We are tasked with finding an equation in the form $ y = mx + b $, where:
- $ x $ is the number of monthly minutes used.
- $ y $ is the total monthly cost.
- $ m $ represents the rate per minute (the slope).
- $ b $ represents the fixed monthly fee (the y-intercept).

We are given two points based on the information:
1. For 280 minutes, the cost is $100. So, we have the point $ (280, 100) $.
2. For 580 minutes, the cost is $175. So, we have the point $ (580, 175) $.

We can use the formula for the slope $ m $:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{175 - 100}{580 - 280} = \frac{75}{300} = 0.25
\]
Thus, $ m = 0.25 $, meaning the cost per minute is $0.25.

Now, we can use the slope-intercept form to find the y-intercept $ b $. Using the point $ (280, 100) $:
\[
y = mx + b \Rightarrow 100 = 0.25(280) + b
\]
\[
100 = 70 + b \Rightarrow b = 100 - 70 = 30
\]

So, the equation is:
\[
y = 0.25x + 30
\]

### B) Using the Equation:
To find the total monthly cost for 912 minutes, we substitute $ x = 912 $ into the equation:
\[
y = 0.25(912) + 30 = 228 + 30 = 258
\]

Thus, the total monthly cost for 912 minutes is **$258**.

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Would you like further clarification or more details?

### Here are 5 related questions:
1. How do you calculate the slope $ m $ between two points?
2. What does the y-intercept represent in the context of this problem?
3. Can you predict the cost for 1000 minutes using the equation?
4. If a customer uses 400 minutes, how much would their total cost be?
5. What happens to the total cost if the number of minutes is reduced by half?

### Tip:
Always verify that the units you're working with in slope problems are consistent. In this case, the slope (rate per minute) should reflect how costs change with respect to minutes.

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 280 minutes, the monthly cost will be $100. If the customer uses 580 minutes, the monthly cost will be $175. 
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 cost of the A Fee and Fee plan.
B) Use your equation to find the total monthly cost if 912 minutes are used.

Learn how to find the linear equation for a cellular plan where the monthly cost depends on minutes used. This problem involves finding the equation in y = mx + b form and using it to calculate the total cost for 912 minutes. Suitable for Grades 8-10.

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