Step-by-step explanation:
the first hint is in the word itself : linear.
it means it is a line. everything goes straight. no changes in the slope.
so, you see already in the graph ; the first table is non-linear, the second one is linear.
a bit more formally and mathematically :
if you look at any pair of points (x1, y1) and (x2, y2) on the curve, the ratio (y2-y1)/(x2-x1) is constant, always the same value. then it is a linear function.
if this changes from 1 pair of points to any other, it is non-linear.
take table 2 :
(16-20)/(6-5) = -4/1 = -4
(12-8)/(7-6) = -4/1 = -4
(12-20)/(7-5) = -8/2 = -4
=> for the observed range it is linear. all the ratios are the same.
but table 1
(2-1)/(1-0) = 1/1 = 1
(5-2)/(2-1) = 3/1 = 3
(5-1)/(2-0) = 4/2 = 2
the ratios are continuously changing.
=> non-linear.
