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Use the table to answer the question.

Number of Months Cost ($)
1 74
2 99
3 124
4 149
The table below shows the cost for a gym membership at the local fitness center with an initial start-up fee charged in the first month. Find the slope, or monthly cost.

1 answer

To find the slope, or the monthly cost, we can use the information from the table provided. The slope represents the change in cost per month.

We can calculate the slope using the formula for slope \( m \):

\[ m = \frac{\text{change in cost}}{\text{change in number of months}} \]

From the table, we can take any two consecutive points to find the slope. Let's use the first two months as an example:

  1. For month 1, the cost is $74.
  2. For month 2, the cost is $99.

Now we can substitute these values into the formula:

\[ m = \frac{99 - 74}{2 - 1} = \frac{25}{1} = 25 \]

The slope (monthly cost) is $25.

We can check this with the other months to ensure consistency:

  • From month 2 to month 3: \[ m = \frac{124 - 99}{3 - 2} = \frac{25}{1} = 25 \]
  • From month 3 to month 4: \[ m = \frac{149 - 124}{4 - 3} = \frac{25}{1} = 25 \]

The slope remains consistent. Therefore, the monthly cost is $25.