A local gym charges a one-time registration fee plus a constant monthly fee. The total cos… — SAT

A local gym charges a one-time registration fee plus a constant monthly fee. The total cost, $C$ , in dollars, for a membership of $m$ months is modeled by the equation $C = 35m + 50$ . What is the one-time registration fee, in dollars, for the gym?

Answer: 50 dollars

Answer

The one-time registration fee is 50 dollars.

In the linear model

C = 35m + 50

, the constant term

50

represents the value of the function when

m = 0

. In this context,

m = 0

corresponds to

0

months of membership, meaning no monthly fees have been incurred yet. Therefore, the value of

50

represents the initial, one-time registration fee.

Step-by-Step Solution

Analyze the linear equation

C = 35m + 50

to identify the slope and the y-intercept.

The slope is

35

(the coefficient of

m

) and the y-intercept is

50

(the constant term).

In a linear equation of the form

y = mx + b

, the constant

b

represents the value of

y

when

x = 0

(the y-intercept), and the coefficient

m

represents the rate of change (the slope).

Interpret the meaning of the y-intercept in the given context.

m = 0

months, the total cost

C

C = 35(0) + 50 = 50

dollars.

The cost at

0

months represents the upfront, one-time fee before any monthly fees are added, which is the registration fee.

Key Concept

Interpreting the y-intercept of a linear function in a real-world context.

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