Question

Graph the function by the table. Is the function linear or nonlinear?

A. Nonlinear

B. Linear

Answer 1

Option A - Non-linear

Explanation:

Given : Graph the function by the table.

x y

1 12.3

2 19.6

3 26.6

4 34.2

5 41.5

To find : Is the function linear or nonlinear?

Solution :

The function is linear when there slopes are equal.

So, we find the slope of the points.

`m=(y_2-y_1)/(x_2-x_1)`

Taking point,
`(x_1,y_1)=(1,12.3)` and
`(x_2,y_2)=(2,19.6)`

`m=(19.6-12.3)/(2-1)`

`m=(7.3)/(1)`

`m=7.3`

Taking point,
`(x_1,y_1)=(2,19.6)` and
`(x_2,y_2)=(3,26.6)`

`m=(26.6-19.6)/(3-2)`

`m=(7)/(1)`

`m=7`

We have seen that slope between points are not equal.

Therefore, The given points are non-linear.

So, Option A is correct.