Answer:
y = -7x + 224
Step-by-step explanation:
First off, the m-value.
The m-value is the constant rate at which something changes. For example, if I had 43 bananas and I subtracted 7 each week, the constant rate at which it changed would be -7. Another way to think about it is the amount of something you subtract per period. According to my last example, you subtract 7 each period, which would be a week. This is also called the slope, which is the rate of change, but I'm assuming you won't analyze these graphs until later. Using the situation presented in the problem, the constant rate at which the gym subtracts from Lucy's account is -$7 per period, which is each time Lucy goes to the gym.
Secondly, the b-value, also known as the y-intercept. This is your starting point. Using my last example, I am starting at 43 bananas. Using the example from the problem, Lucy pays $224 dollars in advance to the gym. So, her starting point is $224.
(you don't need to read this if you don't want to, but it might be helpful!) The reason we use this equation is to be able to find the value of x or y at a given point. X is usually time, which is an independent variable, and y is dependent on the situation. In this one, it is how much money Lucy has spent at the gym. So, for example, if you wanted to find out how many trips to the gym it would take for Lucy to run out of her initial amount, $224, you would plug in 0 for y and solve for x.
0 = -7x + 224 *add 7x to the other side, in order to reverse the negative*
7x = 224 *divide by 7 on both sides*
x = 32 trips to the gym
Another way you could use it is if you wanted to find out how much money Lucy had left after she went to the gym 4 times. You would plug in 4 for x.
y = -7*(4) + 224
y = -28 + 224 *multiply -7 by 4*
y = 224- 28 *adding a negative is like subtracting a positive*
y = $196
Hope this helps!
