Sophia is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The one-time fee to join the gym is $100 and the total cost of membership, including the joining fee, would be $300 for 5 months. Write an equation for C, C, in terms of t, t, representing the total cost of the gym membership over tt months.

c=40t+100

Step-by-step explanation:

Since the one-time fee to join the gym is $100, Sophia would have to pay $100 even for 0 months of membership, meaning C=\color{blue}{100}C=100 when t=\color{green}{0},t=0, which is the y-y−intercept.

(\color{green}{0}, \color{blue}{100})\text{ is a point on the graph}

(0,100) is a point on the graph

Since the total cost of membership over 5 months is $300, we know that C=\color{blue}{300}C=300 when t=\color{green}{5}.t=5.

(\color{green}{5}, \color{blue}{300})\text{ is a point on the graph}

(5,300) is a point on the graph

\text{Find the slope using the two points:}

Find the slope using the two points:

m=\frac{y_2-y_1}{x_2-x_1}=\frac{\color{blue}{300}-\color{blue}{100}}{\color{green}{5}-\color{green}{0}}=\frac{200}{5}=\color{coral}{40}

m=  

x  

2

−x  

1

y  

2

−y  

1

=  

5−0

300−100

=  

5

200

=40