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.

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.