Let's break down the problem step by step.

a. Writing the Linear Equation

The total monthly cost $y$ depends on two factors:

1. A fixed monthly fee of $20.
2. A variable cost of $0.10 per minute of calls, where $x$ is the number of minutes used.

The linear equation that represents this relationship is:

$y = 0.10x + 20$

b. Graphing the Equation

To graph the equation $y = 0.10x + 20$:

1. Plot the y-intercept: Start at the point $(0, 20)$ because when $x = 0$, $y = 20$.
2. Use the slope: The slope is 0.10, which means for every additional minute, the cost increases by $0.10.

To estimate the monthly cost for 150 minutes of calls, substitute $x = 150$ into the equation:

$y = 0.10(150) + 20 = 15 + 20 = 35$

So, the estimated monthly cost for 150 minutes of calls is $35.

c. Explanation of the Slope and Y-Intercept

• Slope (0.10): This represents the cost per minute of calls. For every additional minute, the total cost increases by $0.10.

• Y-intercept (20): This represents the fixed monthly fee. Even if no calls are made (i.e., $x = 0$), the cost will still be $20.

The slope tells you how much the cost changes with each additional minute, while the y-intercept gives the base cost before any calls are made.

Would you like to see the graph of the equation, or do you have any questions?

Here are 5 relative questions for you:

1. How would the equation change if the per-minute cost was $0.15 instead of $0.10?
2. What would the y-intercept be if there were no fixed monthly fee?
3. How would the graph change if the fixed monthly fee increased to $30?
4. What does it mean if the slope of the line was steeper?
5. How can you use this equation to predict the cost for any number of minutes?

Tip: When interpreting a linear equation, the slope always represents the rate of change, while the y-intercept represents the initial value before any changes occur.