Question

1. Is the function described by the points in this table linear or nonlinear?

x y
−3 9
−1 1
0 0
1 1
3 9

A. linear

B. nonlinear

2. Which table contains a set of non-linear ordered pairs?
A.
x y
0 1
1 2
2 3
3 4
B.
x y
0 4
1 7
2 10
3 13
C.
x y
0 7
1 5
2 3
3 1
D.
x y
0 1
1 2
2 5
3 10

3. Is this function linear or nonlinear?

y=3x−5

linear

nonlinear

Answer 1

Answer: 1. Option B

2. Option D

3. Linear

Explanation:

1. In this question coordinates of the points have been given and we have to describe the the function as linear or nonlinear.

As we know for a linear function there should and a constant difference in x and y coordinates of the points given.

Our points are A(-3,-9) B(-1,1) C(0,0) D(1,1) E(3,9)

Now difference in x coordinates of A and B is = (-3)-(-1) = -2

Difference in x coordinates of B and C = (-1)-(0) = -1

This clearly shows that the difference in x coordinates of A,B,C,D,E is not constant.Therefore the function described by these points is non linear.

2. Similarly in this part we find option D in which the points given are (0,1) (1,2) (2,5) (3,10).

In this set of points difference in x coordinates is 1 that is constant but difference in y coordinates is not constant. so the unction is non linear. So option D is the set of non linear ordered pairs.

3. In this part of the question function is y=3x-5

By putting the values of x as 1,2,3( with a constant difference 1) we get the value of y as -2,1,4 which show a common difference of 3 which is constant. Therefore the function is linear.