Question

The following table shows the values of y for different values of x:

x y
0 0
1 1
2 4

Which statement best explains whether the table represents a linear function or a nonlinear function?
A. It represents a linear function because its points are on a straight line.
B. It represents a nonlinear function because its points are not on a straight line.
C.It represents a linear function because its points are not on a straight line.
D. It represents a nonlinear function because its points are on a straight line.

Answer 1

Option B. It represents a nonlinear function because its points are not on a straight line.

Explanation:

Let

`A(0,0),B(1,1),C(2,4)`

we know that

If point A,B and C are on a straight line

then

The slope of AB must be equal to the slope of AC

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

Find the slope AB

`A(0,0),B(1,1)`

substitute in the formula

`m_A_B=(1-0)/(1-0)=1`

Find the slope AC

`A(0,0),C(2,4)`

substitute in the formula

`m_A_C=(4-0)/(2-0)=2`

so

`m_A_B\\eq m_A_C`

Points A, B and C are not on a straight line

therefore

It represents a nonlinear function because its points are not on a straight line