Question

Geoff purchased an annual golf pass for a municipal golf course in his town. He pays a flat fee for the annual golf pass and then each round he plays he must pay the additional cost for a golf cart.

A linear model of this situation contains the values (25, 1172) and (36, 1326), where x represents the number of times he plays each year, and y equals the total amount he spends on golf in one year.
What is the flat fee for the annual golf pass?
A. $822
B. $836
C. $976
D. $14

Answer 1

To find the flat fee for Geoff's annual golf pass, we calculate the slope of the linear model, which gives us the additional cost per round, and then use this to find the y-intercept, which represents the flat fee. The calculation reveals that the flat fee is $822.

Step-by-step explanation:

To determine the flat fee for Geoff's annual golf pass, we need to use the two given points that lie on the line representing the linear model of Geoff's golf expenses. These points are (25, 1172) and (36, 1326), where x is the number of rounds played and y is the total amount spent.

First, we find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Applying the points given:

m = (1326 - 1172) / (36 - 25) = 154 / 11 = 14

This tells us that for each additional round played, Geoff spends an extra $14, which is the cost of the golf cart. Next, we use the slope-intercept form of a linear equation, which is y = mx + b, where b is the y-intercept. This y-intercept represents the annual flat fee, as it will be the expense when Geoff plays 0 rounds. Using one of the points to solve for b:

1172 = 14 * 25 + b
b = 1172 - 350
b = 822

Therefore, the flat fee for the annual golf pass is $822.