Answer:
A school system is reducing the amount of dumpster loads.Required equation is f(x) = -3x + 60.
Solution:
Given that;
School is reducing amount of dumpster loads of trash
Trash is removed each week.
Also the reduction in the amount of waste is in linear relationship with number of week
General form of linear equation is as follows
f(x) = ax + b
Let’s assume our required function is f(x) = ax + b where f(x) represents amount of waste and x represent number of week.
Using first condition that is in week 5, there were 45 dumpster loads of waste removed.
That is substituting x = 5 and f(x) = 45 we get
45 = 5a + b
5a + b = 45 ------ (1)
Similarly for 10th week, x = 10 and f(x) = 30 , we get
30 = 10a + b
10a + b = 30 ------- (2)
On subtracting equation (1) from equation ( 2 ) we get
(10a + b) – (5a + b) = 30 – 45
5a = -15
a = -3
Substitute value of a in equation 1 to get value of b
5 ( -3) + b = 45
b = 60
So we get a = -3 and b = 60.
Finally substituting value of a and b in general linear equation we get our required equation that is f(x) = -3x + 60
