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.

Question

A linear model of this situation contains the values (21 , 949) and (35 , 1,075), 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

To find the flat fee for the annual golf pass, we need to determine the y-intercept of the linear model.

Let's use the first point (21, 949) to find the y-intercept. The y-intercept is the value of y when x is 0.

Using the point-slope form of a linear equation, we have:

y - y1 = m(x - x1)

Let's substitute the values from the first point into the equation:

y - 949 = m(21 - 0)

Simplifying the equation:

y - 949 = 21m

Moving 949 to the other side of the equation:

y = 21m + 949

Now we have an equation in the form y = mx + b, where m represents the slope, and b represents the y-intercept.

Comparing the equation with the slope-intercept form, we can see that the y-intercept is 949.

Therefore, the flat fee for the annual golf pass is 949.