Question

I need some help to tell whether a table is a linear or non linear function

Answer 1

A linear equation has the form:

$y=mx+b$

Let's find a linear equation using the table, and let's check if it satisfy all the points:

$\begin{gathered} x=0,y=-1 \\ -1=b \\ ------ \\ x=1,y=1 \\ 1=m+b \\ 1=m-1 \\ m=2 \end{gathered}$

so:

$y=2x-1$

Let's check the other points:

$\begin{gathered} x=-3 \\ y=2(-3)-1=-6-1=-7_{\text{ }}True \\ ------ \\ x=-2 \\ y=2(-2)-1=-4-1=-5_{\text{ }}True \\ ------ \\ x=-1 \\ y=2(-1)-1=-2-1=-3_{\text{ }}True \end{gathered}$

Therefore, we can conclude it is a linear function.