Let's begin by listing out the given information
[tex]\begin{gathered} g\mleft(x\mright)=\frac{3}{2}x-7 \\ g(x)=y \\ y=\frac{3}{2}x-7 \end{gathered}[/tex]
We will proceed to assume values for x to obtain the y-values (x = -2, 0, 4, 8)
[tex]\begin{gathered} y=\frac{3}{2}x-7 \\ x=-2 \\ y=\frac{3}{2}(-2)-7=-3-7=-10 \\ x=0 \\ y=\frac{3}{2}(0)-7=0-7=-7 \\ x=4 \\ y=\frac{3}{2}(4)-7=6-7=-1 \\ x=8 \\ y=\frac{3}{2}(8)-7=12-7=5 \\ (x,y)=(-2,-10),(0,-7),(4,-1),(8,5) \end{gathered}[/tex]
We will plot these points on the graph. We have:
