Question

dominic is signing up for a gym membership with a one - time fee to join and then a monthly fee to remain a member. the total cost of the gym membership over t months is given by the equation c = 45t+100. what is the y - intercept of the equation and what is its interpretation in the context of the problem? the y - intercept of the function is \boxed{} which represents

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. In the given equation $C = 45t+100$, we can think of $C$ as the dependent variable (similar to $y$) and $t$ as the independent variable (similar to $x$).

Step2: Identify the $y$-intercept

Comparing $C = 45t + 100$ with $y=mx + b$, we can see that when $t = 0$ (which represents the number of months being 0, i.e., the time when Dominic just signs up for the gym), the value of $C$ is $C=45(0)+100=100$. So the $y$-intercept (in terms of the $C - t$ relationship) is 100. In the context of the problem, this $y$-intercept represents the one - time fee to join the gym, because when $t = 0$ (no months of membership have passed), the total cost $C$ is equal to this one - time fee.

Answer:

The $y$-intercept of the equation is 100, which represents the one - time fee to join the gym.