Question

adrian is signing up for a gym membership with a one - time fee to join and then a monthly fee to remain a member. let c represent the total cost of the gym membership over t months. the table below has select values showing the linear relationship between t and c. determine the monthly fee to remain a member.\
\

t	c	\
----	----	\
3	150	\
6	225	\
9	300

Explanation:

Step1: Recall slope formula for linear relation

The monthly fee is the slope of the linear relationship between \( t \) (months) and \( C \) (cost). The slope \( m \) between two points \((t_1, C_1)\) and \((t_2, C_2)\) is given by \( m=\frac{C_2 - C_1}{t_2 - t_1} \).
Take two points, e.g., \((3, 150)\) and \((6, 225)\).

Step2: Calculate the slope (monthly fee)

Substitute \( t_1 = 3, C_1 = 150, t_2 = 6, C_2 = 225 \) into the slope formula:
\( m=\frac{225 - 150}{6 - 3}=\frac{75}{3}=25 \).
We can verify with another pair, say \((6, 225)\) and \((9, 300)\):
\( m=\frac{300 - 225}{9 - 6}=\frac{75}{3}=25 \).

Answer:

The monthly fee to remain a member is \(\$25\).