Question

The total membership cost in dollars, y, at World Fitness Health Club can be represented by the following graph, where x is the number of months of membership. Use the graph to create a linear function when the one time registration fee is $25.

At Purple Experiment Health Club, a member pays y dollars, which includes a one-time registration fee of $15 plus $20 each month, x, they are a member.

Which club will be least expensive if John plans to attend for 8 months?

World Fitness because after 8 months John would have paid $145.

Purple Experiment because after 8 months John would have paid $145.

World Fitness because after 8 months John would have paid $175.

Purple Experiment because after 8 months John would have paid $175.

Answer 1

A. World Fitness because after 8 months John would have paid $145.

Step-by-sep explanation:

✍️To create a linear equation in the slope-intercept form,
`y = mx + b`, we need to determine the value of m and b, using the information provided.

World Fitness Health Club:

Total membership cost in dollars = y

number of months = x

b = y-intercept, which represents the one-time registration fee = $25 (this is where the line intercepts the y-axis)

m = slope of the line of the graph which represents the charges per month.

Using the points on the line, (1, 40) and (3, 70), calculate the value of m.

`m = (y_2 - y_1)/(x_2 - x_1) = (70 - 40)/(3 - 1) = (30)/(2) = 15`

Substitute m = 15, and b = 25 into
`y = mx + b`.

Thus, the linear equation representing total membership cost for World Fitness Health Club would be:

`y = 15x + 25`.

✍️Let's create a linear equation for Purple Experiment Health Club also using the information provided in the question:

Charges per month (m) = 20

One-time registration fee/Y-intercept (b) = 15

Substitute m = 20 and b = 15 into
`y = mx + b`.

Thus, the linear equation representing total membership cost for Purple Experiment Health Club would be:

`y = 20x + 15`.

✍️To determine the club that will be least expensive if John plans to attend for 8 months, find the total cost (y) for each fitness club by substituting x = 8 into each of the linear equation created:

✅Total membership cost for World Fitness Health Club would be:

`y = 15x + 25`

Plug in the value of x

`y = 15(8) + 25 = 120 + 25`

`y = 145`

It would cost John $145 if he attends World Fitness Health Club for 8 months.

✅Total membership cost for Purple Experiment Health Club would be:

`y = 20x + 15`

Plug in the value of x

`y = 20(8) + 15 = 160 + 15`

`y = 175`

It would cost John $175 if he attends Purple Experiment Health Club for 8 months.

✅Therefore, World Fitness Health Club will be least expensive if John plans to attend for 8 months.

The answer: "World Fitness because after 8 months John would have paid $145."