Question

gym plus charters a one time join the plus a monthly membership fee. The total cost is represented on the graph. How can you represent this situation algebraically
the graph shows a y intercept of 50 and a point at (6,140)

Answer 1

To represent the situation algebraically, we can derive a linear equation based on the information given.

The total cost \( C \) can be represented as a function of the number of months \( m \) you have a gym membership.

From your description, we know:

- The y-intercept \( (0, 50) \) represents the one-time join fee. So, the join fee is \( 50 \).
- The graph also gives us another point \( (6, 140) \), which indicates that after 6 months, the total cost is \( 140 \).

We can use the point-slope form of a linear equation to derive the equation that models this situation.

Let’s denote:
- \( C \) as the total cost
- \( m \) as the number of months
- \( b \) as the one-time join fee (which we already know is \( 50 \))
- \( m \) as the monthly membership fee

Now, we can establish two points based on the information we have:

1. The y-intercept (0, 50)
2. The point (6, 140)

The general form of the linear equation is given by:
\[
C = m \cdot T + b
\]
Where \( T \) is the number of months.

From the point (6, 140):
\[
140 = 6m + 50
\]

Now, we can solve for \( m \):
\[
140 - 50 = 6m
\]
\[
90 = 6m
\]
\[
m = 15
\]

Now that we have \( m \), we can plug it back into the model:
\[
C = 15T + 50
\]

Thus, the total cost \( C \) in terms of the number of months \( T \) is:
\[
C = 15T + 50
\]

Where:
- \( 50 \) is the one-time join fee,
- \( 15 \) is the monthly membership fee.