Answer :
The general equation in slope intercept form is given by
[tex]\begin{gathered} y=mx+c \\ \text{where y is the slope and c is the y intercept} \end{gathered}[/tex]The given equation is
[tex]\begin{gathered} 3x-2y=12 \\ \text{Rewrite the equation by adding 2y to both sides} \\ 3x-2y+2y=12+2y \\ 3x=12+2y \\ \text{Subtract 12from both sides} \\ 3x-12=12-12+2y \\ 3x-12=2y \\ \text{Divide both sides by 2 } \\ \frac{3}{2}x-6=y \\ y=\frac{3}{2}x-6 \\ \text{where }\frac{3}{2}\text{ is the slope and -6 is the y intercept comparing it with y=mx+c} \end{gathered}[/tex]Put y=0 to the equation to get the x intercept.
[tex]\begin{gathered} 0=\frac{3}{2}x-6 \\ \frac{3}{2}x=6 \\ x=\frac{6\ast2}{3}=4 \end{gathered}[/tex]Now plot the graph by joining coordinates of y intercept (0,-6) and coordinates of x intercept (4,0)
