Question

what is an equation of the line that passes through the point (-2,-3) and is parallel to the line x+3y=24

Answer 1

Solve first for the slope intercept form for the equation x + 3y = 24.

`\begin{gathered} \text{The slope intercept form is }y=mx+b \\ \text{Convert }x+3y=24\text{ to slope intercept form} \\ x+3y=24 \\ 3y=-x+24 \\ (3y)/(3)=(-x)/(3)+(24)/(3) \\ y=-(1)/(3)x+8 \\ \\ \text{In the slope intercept form }y=mx+b,\text{ m is the slope. Therefore, the slope of} \\ y=-(1)/(3)x+8,\text{ is }-(1)/(3)\text{ or } \\ m=-(1)/(3) \end{gathered}`

Since they are parallel, then they should have the same slope m. We now solve for b using the point (-2,-3)

`\begin{gathered} (-2,-3)\rightarrow(x,y) \\ \text{Therefore} \\ x=-2 \\ y=-3 \\ \text{and as solved earlier, }m=-(1)/(3) \\ \\ \text{Substitute the values to the slope intercept form} \\ y=mx+b \\ -3=(-(1)/(3))(-2)+b \\ -3=(2)/(3)+b \\ -3-(2)/(3)=b \\ (-9-2)/(3)=b \\ b=-(11)/(3) \end{gathered}`

After solving for b, complete the equation.

`y=-(1)/(3)x-(11)/(3)\text{ (final answer)}`