Here's a way to show that x^2 - 2 is not linear
Let x = 0 ....then (0)^2 - 2 = -2
And
Let x = 2 ....then (2)^2 - 2 = 2
And
Let x = -2 ....then (-2)^2 - 2 = 2
So the points (0, -2), ( 2, 2) and (-2,2) are on the graph
Now the slope between the frist two points = 2 while the slope beween the second and third point = 0.......but....the slope beween any two points on a line is always the same
Thus, x^2 - 2 cannot be linear......