Question

8. Do the following tables represent a linear or non-linear relationship?

Answer 1

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.

Answer 2

Answer:

the first table is a non-linear relationship and the second table is a linear relation ship because the first table as a curve in its line and it is not straight making it non-linear the second table is linear because it forms a straight line making it linear

Step-by-step explanation:

to find a linear relationship place the points on the graph. then if the they form a straight line then your table is linear

Also to find a nonlinear relation ship place the points that are given to you on a graph and if they are not a straight line then they are a nonlinear relationship