Question

when a linear function is graphed it passes through the points (-1,1), (1,5), and (3,9) what is the rate of change for the function?

Answer 1

Use the linear slope formula to solve for m: 

m=(y2-y1)/(x2-x1)

using the points (-1,1) and (1,5) you can find the slope for the first interval:
 
m=(5-1)/(1-(-1))
m=4/2
m=2

you can double check by using the same formula on the second interval, which is (1,5) to (3,9).

m=(9-5)/(3-1)
m=4/2
m=2 

therefore, the rate of change is 2.