Math Problem Statement
Solution
The problem states that Kari pays a fixed initial fee plus a monthly fee for a game. The cost over time months is represented by the linear equation:
Here:
- is the number of months.
- is the total cost in dollars.
Step 1: Fill in the Table
Let's calculate for each value of (2, 5, 6, and 12 months).
-
For :
-
For :
-
For :
-
For :
The completed table would look like this:
(months) | (Total Cost) |
---|---|
2 | 64 |
5 | 100 |
6 | 112 |
12 | 184 |
Step 2: Create the Graph
Using this table, you can plot the points on a graph with:
- The x-axis representing the number of months .
- The y-axis representing the total cost .
Explanation for the Graph
The line will be straight, following the linear equation . 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:
- How would the total cost change if the monthly fee increased?
- What would the equation look like if the initial fee was different?
- How does the graph change if the monthly rate changes from $12 to $15?
- What is the total cost after 24 months?
- 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.
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Math Problem Analysis
Mathematical Concepts
Linear equations
Algebra
Graphing
Formulas
C = 12m + 40
Theorems
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Suitable Grade Level
Grades 6-8