Question

What is the equation of the line that passes through the point (6, 1) and is perpendicular to the line y = –3x + 2

Answer 1

if the lines perpendicular each other then \[m _{1}m _{2}=-1\]
we know second line`s slop is -3 ( because y=ax+b then m=a)
\[m _{1}(-3)=-1\]
\[m _{1}=1/3\]
if we know slop and one point we can find the equation
\[m=\frac{y-y _{1}}{x-x _{1}}\]
\[\frac{1}{3}=\frac{y -1}{x -6}\]
\[x-6=y-1\]
\[y=x-5\]