Answer:
Perpendicular lines are lines that are at right angles to each other.
For perpendicular lines, the product of their slopes is -1.
[tex]\implies m_2=\dfrac{-1}{m_1}[/tex]
(where [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of perpendicular lines)
The slope of the given equation is -3. Therefore, to find the slope of the line that is perpendicular:
[tex]m_2=\dfrac{-1}{-3}=\dfrac13[/tex]
Now we have the slope, we can use the point-slope form of a linear equation with [tex]m=\dfrac13[/tex] and [tex](x_1,y_1)=(2,-6)[/tex] to find the equation of the perpendicular line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-6)=\dfrac13(x-2)[/tex]
[tex]\implies y+6=\dfrac13x-\dfrac23[/tex]
[tex]\implies y=\dfrac13x-\dfrac{20}3[/tex]
