Answer
See graph
Work Step by Step
Given\begin{equation}
4 x-3 y<12.
\end{equation} Rewrite the inequality so that $y$ is a function of $x$. \begin{equation}
\begin{aligned}
4 x-3 y&<12\\
y&>\frac{12-4x}{-3}\\
y&> \frac{4}{3} x-4.
\end{aligned}
\end{equation} We notice that $y=\frac{4}{3}x-4$ is a linear function with no restriction on the domain. The domain is all real numbers. The intercepts are \begin{equation}
\begin{aligned}
x&=0\implies y= -4 \\
y&= 0\implies x= 3.
\end{aligned}
\end{equation} The graph of the function is shown in the figure below with both intercepts labelled. The graph of the line is drawn with a dashed line and shaded above the line because the inequality is a greater than inequality with no ''equal to '' part.
