Question

A public golf course charges a ​$400 annual fee to belong to its club. Members of the club pay $40 to play a round of golf. The equation that gives the cost​ y = 400 +40x to belong to the club and to play x rounds of golf per year is yx.

​a) Find the​ y-intercept of this equation.
​b) Find the​ x-intercept in the context of this problem.
​c) Find the total cost for a club member who plays rounds of golf.

Answer 1

The y-intercept of the equation is 400, the x-intercept is -10, and the total cost for a club member is given by the equation y = 400 + 40x.

Step-by-step explanation:

The y-intercept of the equation y = 400 + 40x is the value of y when x = 0. In this equation, the y-intercept is 400, which represents the annual fee to belong to the club.

(a) The y-intercept is 400.

The x-intercept of the equation y = 400 + 40x is the value of x when y = 0. In this context, the x-intercept represents the number of rounds of golf a club member can play for free. To find the x-intercept, we set y = 0 and solve for x: 0 = 400 + 40x. Solving for x, we get x = -10.

(b) The x-intercept in this problem is -10, which means that a club member can play 10 rounds of golf for free.

To find the total cost for a club member who plays x rounds of golf, we substitute the value of x into the equation y = 400 + 40x. For example, if x = 5, the total cost would be y = 400 + 40(5) = 400 + 200 = 600. (c) The total cost for a club member who plays rounds of golf is given by the equation y = 400 + 40x.