91Ó°ÊÓ

The given equation is

$y=3x+1$

Substitute $x=-1$in the equation

$$\begin{gathered} y=3x+1 \\ y=3(-1)+1 \\ y=-3+1 \\ y=-2 \end{gathered}$$

So the solution to the equation is$(-1,-2)$

Substitute $x=0$in the equation

role="math" localid="1647469599542" $$\begin{gathered} y=3x+1 \\ y=3\left(0\right)+1 \\ y=0+1 \\ y=1 \end{gathered}$$

So the solution to the equation is$(0,1)$

Substitute $x=1$in the equation

$$\begin{gathered} y=3x+1 \\ y=3\left(1\right)+1 \\ y=3+1 \\ y=4 \end{gathered}$$

So the solution to the equation is$(1,4)$

To check $(-1,-2),$substitute in the equation

$$\begin{gathered} y=3x+1 \\ -2\stackrel{?}{=}3(-1)+1 \\ -2=-2 \end{gathered}$$

The left-hand side is equal to the right-hand side, so $(-1,-2)$is a solution to the equation.

To check$(0,1)$ substitute in the equation

$$\begin{gathered} y=3x+1 \\ 1\stackrel{?}{=}3\left(0\right)+1 \\ 1=1 \end{gathered}$$

The left-hand side is equal to the right-hand side, so $(0,1)$is a solution to the equation.

To check $(1,4)$substitute in the equation

$$\begin{gathered} y=3x+1 \\ 4\stackrel{?}{=}3\left(1\right)+1 \\ 4=4 \end{gathered}$$

The left-hand side is equal to the right-hand side, so $(1,4)$is a solution to the equation.

So $(-1,-2),(0,1),\&(1,4)$are solutions to the equation.