Question

Find the equation for the line parallel to 3y-9x=9 and goes through the point (-2,-6) Write the answer in the form y=mx+b

Answer 1

`\begin{gathered} \text{FInd the slope of the first equation,} \\ 3y-9x=9 \\ 3y=9x+9 \\ (3y)/(3)=(9x+9)/(3) \\ y=3x+3 \\ \text{In the form }y=mx+b,\; m\text{ is the slope. Therefore, }m=3 \end{gathered}`
`\begin{gathered} \text{Since the two lines are parallel, they have the same slope. Solve for b,} \\ \text{using the point (-2,-6)} \\ (x,y)\rightarrow(-2,-6) \\ y=mx+b \\ -6=(3)(-2)+b \\ -6=-6+b \\ -6+6=b \\ 0=b\rightarrow b=0 \end{gathered}`
`\begin{gathered} \text{Now that we know }b=0\text{ and }m=3,\text{ complete the equation} \\ y=mx+b \\ y=(3)x+(0) \\ y=3x\text{ (final answer)} \end{gathered}`