Question

Amanda pays a membership fee of 100 to join a gym along with a monthly fee of 15. The equation y = 100 + 15x represents the total cost, y, of her membership in x months. a. What is the y-intercept? What does it represent? b. What is the slope? What does it represent?

Answer 1

a. The y-intercept is 100, representing the initial cost of joining the gym, which is the membership fee.

b. The slope is 15, representing the monthly cost of the gym membership.

Step-by-step explanation:

The y-intercept, which is the value of y when x is zero, is 100 in this equation. In the context of Amanda's gym membership, this 100 represents the initial cost she incurs when joining the gym, which is the membership fee. Essentially, even if Amanda doesn't use the gym at all (x=0), she still has to pay this fixed amount of 100 for the membership.

On the other hand, the slope of the equation is 15. In this context, the slope represents the rate of change in the total cost per month. So, for every additional month (x), Amanda incurs an extra 15 in fees. This reflects the monthly cost of maintaining her gym membership.

To put it simply, the y-intercept is the starting point, the initial cost of joining the gym, while the slope is the ongoing rate at which the monthly costs accumulate. So, Amanda's total cost (y) is determined by both the fixed initial cost and the variable monthly cost, as represented by the y = 100 + 15x equation.

Answer 2

a. The y-intercept is 100, representing the initial cost of joining the gym, which is the membership fee.

b. The slope is 15, representing the monthly cost of the gym membership.

Step-by-step explanation:

The y-intercept, which is the value of y when x is zero, is 100 in this equation. In the context of Amanda's gym membership, this 100 represents the initial cost she incurs when joining the gym, which is the membership fee. Essentially, even if Amanda doesn't use the gym at all (x=0), she still has to pay this fixed amount of 100 for the membership.

On the other hand, the slope of the equation is 15. In this context, the slope represents the rate of change in the total cost per month. So, for every additional month (x), Amanda incurs an extra 15 in fees. This reflects the monthly cost of maintaining her gym membership.

To put it simply, the y-intercept is the starting point, the initial cost of joining the gym, while the slope is the ongoing rate at which the monthly costs accumulate. So, Amanda's total cost (y) is determined by both the fixed initial cost and the variable monthly cost, as represented by the y = 100 + 15x equation.