cant seem to get this

Question

A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.

Answer 1

Lets describe our function in the form y=f(x)

 

The input should be the time, or week that we are in, and the output should be the number of dumpster loads removed that week!

 

We then see that the two data points that are given (45loads in week5 and 30loads in week10) correspond to 

 

f(5)=45 and f(10)=30.

 

If we have a line then y=f(x)=mx+b for some slope m and some y-int b.

 

f(5) = 5m+b =45

f(10) = 10m+b=30

 

Subtracting the first from the second yield: 5m=-15, and so the slope is -3, and plugging this back into the first equation, gives 5(-3)+b=45, so b=60

 

Thus the linear equation we seek if f(x)=-3x+60.

 

Given points in the plane of (5,45) and (10,30) we could use a variety of techniques to find the slope and y-intercept and write a linear equation for this function.  This is simply just one of many approaches to solving this problem.