To find the linear equation, we use two points from the table (1, -3) and (3, -11). First, we have to find the slope with the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=1 \\ x_2=3 \\ y_1=-3 \\ y_2=-11 \end{gathered}[/tex]Let's those coordinates to find the slope.
[tex]\begin{gathered} m=\frac{-11-(-3)_{}}{3-1}=\frac{-11+3}{2}=\frac{-8}{2}=-4\to m=-4 \\ \end{gathered}[/tex]The slope is -4.
Now, we use the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-4(x-1) \\ y+3=-4x+4 \end{gathered}[/tex]Now, we solve for y to express it in slope-intercept form.
[tex]\begin{gathered} y+3=-4x+4 \\ y=-4x+4-3 \\ y=-4x+1 \end{gathered}[/tex]