Explanation:
We were given the equation:
[tex]-8x-3y=-12[/tex]
The slope-intercept is represented by:
[tex]\begin{gathered} y=mx+b \\ where: \\ m=slope \\ b=y-intercept \end{gathered}[/tex]
Rewriting the equation into its slope-intercept form, we have:
[tex]\begin{gathered} -8x-3y=-12 \\ \text{Add ''8x'' to both sides, we have:} \\ -3y=8x-12 \\ \text{Divide both sides by ''-3'', we have:} \\ \frac{-3}{-3}y=\frac{8}{-3}x-\frac{12}{-3} \\ y=-\frac{8}{3}x+4 \end{gathered}[/tex]
Therefore, the equation in slope-intercept is: y = -(8/3)x + 4
We will now input assumed values for "x" to obtain corresponding y-values. We have:
[tex]\begin{gathered} y=-\frac{8}{3}x+4 \\ \\ when:x=-6 \\ y=-\frac{8}{3}(-6)+4=16+4=20 \\ when:x=-3 \\ y=-\frac{8}{3}(-3)+4=8+4=12 \\ \\ when:x=0 \\ y=-\frac{8}{3}(0)+4=0+4=4 \\ \\ when:x=3 \\ y=-\frac{8}{3}(3)+4=-8+4=-4 \\ \\ when:x=6 \\ y=-\frac{8}{3}(6)+4=-16+4=-12 \end{gathered}[/tex]
We will proceed to plot these points on the graph, we have:
