Question

Justin is joining a gym the gym is offering a discount on the fee to join and on the monthly rate the discounted price in dollars the gym charges can be represented by the equation Y equals 10 X +5

Part A what are the slope and the Y intercept of the equation what do the slope and y-intercept each represent in this situation ?.

Part B the regular price in dollar the gym charges can be represented by the equation Y equals 15 X +20. How much money in dollars does Justin save the first month by joining the gym at the discounted price rather than the regular price


Part C Justin create a system of equation based on the equation from part a and the equation from part B, the solution to the system of equation is (-3, -25) Why is the point (-3, ,-25) not possible solution in this solution ?

Answer 1

Part A:

The equation Y = 10X + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, in this equation, the slope is 10 and the y-intercept is 5.

The slope represents the rate of change in the monthly rate of the gym membership. For every one unit increase in the number of months, the monthly rate will increase by $10. The y-intercept represents the initial cost of joining the gym, which is $5.

Part B:

To find out how much money Justin saves the first month by joining the gym at the discounted price, we need to calculate the difference between the regular price and the discounted price for the first month.

The regular price for the first month can be found by plugging in X = 1 into the equation Y = 15X + 20, which gives Y = 35.

The discounted price for the first month can be found by plugging in X = 1 into the equation Y = 10X + 5, which gives Y = 15.

Therefore, Justin saves $20 (35 - 15) the first month by joining the gym at the discounted price rather than the regular price.

Part C:

The system of equations is:

Y = 10X + 5 (discounted price)

Y = 15X + 20 (regular price)

The solution to the system of equations is (-3, -25), which means that if X = -3, then Y = -25 is a solution to both equations. However, this solution is not possible in this situation because X represents the number of months, which cannot be negative. Therefore, the point (-3, -25) is not a valid solution.