Question

a gym charges a membership fee plus an additional fee per yoga class. the table shows the linear relationship between the number of yoga classes taken and the total cost including the membership fee. yoga classes number of yoga classes total cost 6 $67.50 8 $75.00 10 $82.50 14 $97.50 20 $120.00 which statement is true? the additional fee per yoga class is $3.75. the additional fee per yoga class is $8.25. the membership fee is $35.00. the membership fee is $42.50

Explanation:

Step1: Find the cost - increase per class

Let the number of yoga classes be $x$ and the total cost be $y$. The relationship is linear, and the slope $m$ of the line $y = mx + b$ (where $m$ is the cost per class and $b$ is the membership fee) can be found using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Take two points, say $(x_1,y_1)=(6,67.50)$ and $(x_2,y_2)=(8,75.00)$. Then $m=\frac{75 - 67.50}{8 - 6}=\frac{7.5}{2}=3.75$.

Step2: Find the membership fee

Use the point - slope form $y=mx + b$. Substitute $m = 3.75$, $x = 6$ and $y=67.50$ into $y=mx + b$. We get $67.50=3.75\times6 + b$. Then $67.50 = 22.5+b$. Solving for $b$, we subtract 22.5 from both sides: $b=67.50 - 22.5=45$.

Answer:

The additional fee per yoga class is $\$3.75$.