Question

23 it costs $25 to join a gym. the monthly fee is $25. write and graph an equation in two variables that represents the total cost of a gym membership.
equation
(there is a table with x and y columns and a coordinate grid for graphing)

Explanation:

Step1: Define Variables

Let \( x \) be the number of months, and \( y \) be the total cost (in dollars). The joining fee is a one - time cost of \( \$25 \), and the monthly fee is \( \$25 \) per month. So the total cost \( y \) is the sum of the joining fee and the monthly fees. The monthly fee for \( x \) months is \( 25x \) dollars. So the equation is \( y=25 + 25x \) (or \( y = 25x+25 \)).

Step2: Create a Table of Values

We can choose some values for \( x \) (number of months) and find the corresponding \( y \) (total cost).

• When \( x = 0 \) (0 months, just the joining fee), \( y=25(0)+25=25 \).
• When \( x = 1 \) (1 month), \( y=25(1)+25 = 50 \).
• When \( x = 2 \) (2 months), \( y=25(2)+25=75 \).
• When \( x = 3 \) (3 months), \( y=25(3)+25 = 100 \).

Step3: Graph the Equation

To graph the equation \( y = 25x + 25 \), we can use the points from the table. The equation is in the slope - intercept form \( y=mx + b \), where the slope \( m = 25 \) and the y - intercept \( b = 25 \). We plot the points \((0,25)\), \((1,50)\), \((2,75)\), \((3,100)\) on the coordinate plane (with \( x \) as the horizontal axis representing the number of months and \( y \) as the vertical axis representing the total cost) and draw a straight line through them.

Answer:

The equation is \( y = 25x+25 \) (where \( x \) is the number of months and \( y \) is the total cost in dollars). To graph it, plot the points from the table (e.g., \((0,25)\), \((1,50)\), \((2,75)\), \((3,100)\)) and draw a line through them.