The problem states that Kari pays a fixed initial fee plus a monthly fee for a game. The cost $C$ over time $m$ months is represented by the linear equation:

$C = 12m + 40$

Here:

• $m$ is the number of months.
• $C$ is the total cost in dollars.

Step 1: Fill in the Table

Let's calculate $C$ for each value of $m$ (2, 5, 6, and 12 months).

1. For $m = 2$: $C = 12 \times 2 + 40 = 24 + 40 = 64$

2. For $m = 5$: $C = 12 \times 5 + 40 = 60 + 40 = 100$

3. For $m = 6$: $C = 12 \times 6 + 40 = 72 + 40 = 112$

4. For $m = 12$: $C = 12 \times 12 + 40 = 144 + 40 = 184$

The completed table would look like this:

Step 2: Create the Graph

Using this table, you can plot the points $(m, C)$ on a graph with:

• The x-axis representing the number of months $m$.
• The y-axis representing the total cost $C$.

Explanation for the Graph

The line will be straight, following the linear equation $C = 12m + 40$. Each month, the cost increases by $12. Starting from an initial cost of $40, the slope (or rate of change) is $12 per month.

Would you like me to generate a plot for this data?

Additional Questions:

1. How would the total cost change if the monthly fee increased?
2. What would the equation look like if the initial fee was different?
3. How does the graph change if the monthly rate changes from $12 to $15?
4. What is the total cost after 24 months?
5. How would you interpret the slope and intercept in real-life terms?

Tip:

In a linear equation like this, the slope represents the rate of change per month, and the intercept is the initial fixed cost.