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

$y=\frac{x}{3}+17$

Explanation

Step 1

isolate y from the equation to get the form

$y=mx+b$$\begin{gathered} -2x+6y=18 \\ 6y=18+2x \\ y=\frac{18}{6}+\frac{2}{6}x \\ y=\frac{1}{3}x+3\rightarrow y=mx+b \\ \text{Hence} \\ m_1=\frac{1}{3} \end{gathered}$

Now, the lines are perpendicular,so

$\begin{gathered} m_1\cdot m_2=-1 \\ \text{replacing} \\ \frac{1}{3}\cdot m_2=-1 \\ m_2=-3 \end{gathered}$

Step 2

find the equation using

P(9,20)

slope=-3

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

I hope this helps you