Question

12 mr. weiss has decided he needs a gym membership. the following graph was given to mr. weiss, showing the cost for a membership based on number of months. write an equation for the graph in which y represents the total cost based on the number of months x. club northwest (cost of membership) 700 650 600 550 500 (6,500) 450 400 cost ($) 350 300 250 (0, 200) 200 150 100 50 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 months

Explanation:

Step1: Identify the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). We have points \((0, 200)\) and \((6, 500)\).

Step2: Calculate the slope

Substitute into the slope formula: \( m = \frac{500 - 200}{6 - 0} = \frac{300}{6} = 50 \).

Step3: Identify the y - intercept

The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the point \((0, 200)\), \( b = 200 \).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \( y = mx + b \). Substituting \( m = 50 \) and \( b = 200 \), we get \( y = 50x + 200 \).

Answer:

\( y = 50x + 200 \)