Question

For the following situation, (a) write an equation in the form y=mx+b, (b) find and interpret the ordered pair associated with the equation for x=5, and (c) answer the question.A health club membership costs $80, plus $48 per month. Let x represent the number of months and y represent the cost in dollars. How much does the first year’s membership cost?

Answer 1

Based on the question, a health club membership costs $80, plus $48 per month. This can be written as $80 + $48 per month = health membership cost.

If x = month and y = cost, then we can rewrite the equation as:

`\begin{gathered} 80+48x=y \\ or \\ y=48x+80 \end{gathered}`

a. This is our equation in the form of y = mx + b. (y = 48x + 80).

b. If the number of months is 5 or x = 5, we can solve for the total cost of membership by replacing "x" with "5" in the equation.

`\begin{gathered} y=48x+80 \\ y=48(5)+80 \\ y=240+80 \\ y=320 \end{gathered}`

The ordered pair is (5, 320).

This ordered pair indicates that the cost for 5-month membership is $320.

c. Since there are 12 months in 1 year, replace "x" in the equation with 12 and then, solve.

`\begin{gathered} y=48x+80 \\ y=48(12)+80 \\ y=576+80 \\ y=656 \end{gathered}`

Therefore, the first year's membership cost is $656.