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 (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?
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.