Question

Graph each equation rewrite in slope intercept form first if necessary.-8x-3y=-12

Answer 1

Step-by-step explanation:

We were given the equation:

`-8x-3y=-12`

The slope-intercept is represented by:

`\begin{gathered} y=mx+b \\ where: \\ m=slope \\ b=y-intercept \end{gathered}`

Rewriting the equation into its slope-intercept form, we have:

`\begin{gathered} -8x-3y=-12 \\ \text{Add ''8x'' to both sides, we have:} \\ -3y=8x-12 \\ \text{Divide both sides by ''-3'', we have:} \\ (-3)/(-3)y=(8)/(-3)x-(12)/(-3) \\ y=-(8)/(3)x+4 \end{gathered}`

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:

`\begin{gathered} y=-(8)/(3)x+4 \\ \\ when:x=-6 \\ y=-(8)/(3)(-6)+4=16+4=20 \\ when:x=-3 \\ y=-(8)/(3)(-3)+4=8+4=12 \\ \\ when:x=0 \\ y=-(8)/(3)(0)+4=0+4=4 \\ \\ when:x=3 \\ y=-(8)/(3)(3)+4=-8+4=-4 \\ \\ when:x=6 \\ y=-(8)/(3)(6)+4=-16+4=-12 \end{gathered}`

We will proceed to plot these points on the graph, we have: