The problem asks to find the monthly cost for 37 minutes of calls, given the following information:

• The relationship between the calling time (in minutes) and monthly cost (in dollars) is a linear function.
• The slope of the line is $0.12$, meaning the cost increases by 12 cents for each additional minute.
• The monthly cost for 42 minutes of calls is $12.12.

Linear Equation Setup:

We know the slope is $m = 0.12$ and we have the point $(42, 12.12)$. The general equation of a line is:

$y = mx + b$

Where:

• $y$ is the monthly cost,
• $x$ is the calling time,
• $m = 0.12$ is the slope, and
• $b$ is the y-intercept (fixed base cost).

Step 1: Find the y-intercept $b$

Using the known point $(42, 12.12)$:

$12.12 = 0.12 \times 42 + b$

Solve for $b$:

$12.12 = 5.04 + b$ $b = 12.12 - 5.04 = 7.08$

So the equation of the line is:

$y = 0.12x + 7.08$

Step 2: Calculate the cost for 37 minutes of calls

Now, substitute $x = 37$ into the equation:

$y = 0.12 \times 37 + 7.08$ $y = 4.44 + 7.08$ $y = 11.52$

The monthly cost for 37 minutes of calls is $11.52.

Let me know if you need more details or have any questions!

Related Questions:

1. What is the cost for 50 minutes of calls?
2. How would the cost change if the slope increased to 0.15?
3. What does the y-intercept of 7.08 represent in this context?
4. How many minutes would result in a monthly cost of $15?
5. What would the monthly cost be for 0 minutes of calls?

Tip:

The slope of the line represents the rate of change, which in this case is the cost per minute of calls.