Rewrite the equation of the boundary line in the slope intercept form. In order to do that, solve for y:
[tex]\begin{gathered} -5x+3y=-12 \\ 3y=5x-12 \\ y=\frac{5}{3}x-4 \end{gathered}[/tex]
Since the boundary line is continuous and the area is below the line, then:
[tex]y\leq\frac{5}{3}x-4[/tex]
