Question

The cost of belonging to a gym can be modeled by the function C(m)=50m+79.50, where C(m) is the total cost for m months of gym membership. State the values and meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership

Answer 1

Slope = 50 [monthly cost is $50 per month]

Y-Intercept = 79.50 [this is the initial cost of the membership, $79.50]

Explanation:

The equation is:

`C(m)=50m+79.50`

This follows the general function y = mx + b

Where m is the slope and b is the y-intercept.

So, matching coefficients, we see that:

Slope = 50

Y-Intercept = 79.50

THe meaning of slope is for every change in x-values, we have a change of m in y value. Thus, for every change in m (1 month), we will have change of 40 in y-value (which is the cost)

Thus, monthly cost is $50 per month.

Now, y intercept means the value of y(cost) at x = 0 (which is months = 0).

Thus, we can say when months = 0, initially, the cost is 79.50. So, this is teh initial cost of joining the gym.