First, let's express the equation in the slope-intercept form. In order to do it, we need to solve the equation for y:
[tex]\begin{gathered} 4x-3y=6 \\ 3y=4x-6 \\ y=\frac{4}{3}x-2 \end{gathered}[/tex]
Let's evaluate the equation for:
x = -6, -3 , 0, 3, 6
so:
[tex]\begin{gathered} y(-6)=\frac{4}{3}(-6)-2=-8-2=-10 \\ y(-3)=\frac{4}{3}(-3)-2=-4-2=-6 \\ y(0)=\frac{4}{3}(0)-2=0-2=-2 \\ y(3)=\frac{4}{3}(3)-2=4-2=2 \\ y(6)=\frac{4}{3}(6)-2=8-2=6 \end{gathered}[/tex]
Now, we can create the table:
The graph is the following:
