Question

how do i tell if my graph is linear or nonlinear...

Answer 1

Linear means the points lie on a straight line.

Answer 2

If you are given the (x,y) coordinates of points, then you can proceed as follows:
Say you are given these four points. Is the graph of these points linear?
(1,1) (2,2) (3,3) (4,5)

First fit a line to two of the points (any two, I will take the first two)

y = 1 x + 0 or y = x goes through the first two. (I will let you figure out why :)
Now if the other two points are on that line, the graph is linear.
So try the third point
3 = 3 sure enough, so the graph of the first three points would be linear, but the fourth has to be on the line as well.
5 = 4 Whoops, no, that point does not fit our line at all! Therefore the graph of the four points is NOT linear.