Use the table to answer the question.

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 point)
Responses

$49
$49

$25
$25

$74
$74

$37.25
$37.25
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Answer 1

To find the slope (monthly cost) of the gym membership, we can use the values given in the table.

We can observe the costs for each month:

1 month: $74
2 months: $99
3 months: $124
4 months: $149

To calculate the monthly cost (slope), we can find the change in cost divided by the change in number of months between any two points.

For example, using the first two months:

Change in cost = Cost for 2 months - Cost for 1 month
Change in cost = $99 - $74 = $25

Change in months = 2 - 1 = 1

So, the slope (monthly cost) is:
\[ \text{slope} = \frac{\text{Change in cost}}{\text{Change in months}} = \frac{25}{1} = 25 \]

Repeating this process using the second and third months, we get:

Change in cost = Cost for 3 months - Cost for 2 months
Change in cost = $124 - $99 = $25

Change in months = 3 - 2 = 1

So, the slope is again \( 25 \).

Finally, with the third and fourth months:

Change in cost = Cost for 4 months - Cost for 3 months
Change in cost = $149 - $124 = $25

Change in months = 4 - 3 = 1

Thus, the slope remains \( 25 \).

Therefore, the monthly cost is $25.