Question

what is the equation of a line that is perpendicular to -2x+6y=18 and goes through (9,20) in slope intercept form

Answer 1

`y=(x)/(3)+17`

Step-by-step explanation

Step 1

isolate y from the equation to get the form

`y=mx+b`
`\begin{gathered} -2x+6y=18 \\ 6y=18+2x \\ y=(18)/(6)+(2)/(6)x \\ y=(1)/(3)x+3\rightarrow y=mx+b \\ \text{Hence} \\ m_1=(1)/(3) \end{gathered}`

Now, the lines are perpendicular,so

`\begin{gathered} m_1\cdot m_2=-1 \\ \text{replacing} \\ (1)/(3)\cdot m_2=-1 \\ m_2=-3 \end{gathered}`

Step 2

find the equation using

P(9,20)

slope=-3

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-20=(1)/(3)(x-9) \\ y-20=(x)/(3)-(9)/(3) \\ y=(x)/(3)-3+20 \\ y=(x)/(3)+17 \end{gathered}`

I hope this helps you