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 (30, 1,181) and (44, 1,363), 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?

Answer 1

The answer is $760

Explanation:

First, find the rate of change, or slope, from the two given points.

Next, find the equation for the linear model using the slope and a point.

The initial value is the value of y when x equals 0.

In this case, the initial value is the flat fee for the annual golf pass.

Therefore, the flat fee for the annual golf pass is $760.

Answer 2

$791

Explanation:

Find the equation of the line passing thru (30, 1,181) and (44, 1,363), The y-intercept of this equation will answer this question: it represents the annual golf pass.

Moving from (30, 1,181) to (44, 1,363), we see x increasing by 14 from 30 to 44 and y increasing by 182 from 1181 to 1363.

Thus, the slope of this line is m = rise / run = 182 / 14 = 13.

Subst. the knowns (30, 1,181) and m = 13 into the standard equation for a straight line in slope-intercept form, y = mx + b, we get:

1181 = 13(30) + b. Then 1181 - 390 = 791.

The flat fee is $791, payable at the beginning of each year.