Answer:
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
