Respuesta :
If two lines are perpendicular, the multiplication of the slopes is equal to -1.
So, the line x = -3y + 6 can be written as:
[tex]\begin{gathered} x=-3y+6 \\ x-6=-3y \\ \frac{x-6}{-3}=y \\ \frac{-1}{3}x+2=y \end{gathered}[/tex]So, the slope is -1/3. It means that the slope of the perpendicular line is:
[tex]\begin{gathered} \frac{-1}{3}\cdot m=-1 \\ -m=-3 \\ m=3 \end{gathered}[/tex]Then, with a point (x1, y1) and a slope m, we can find the equation of the line as:
[tex]y-y_1=m(x-x_1)[/tex]Replacing, m by 3 and (x1, y1) by (-7,-1), we get:
[tex]\begin{gathered} y-(-1)=3(x-(-7)) \\ y+1=3(x+7) \\ y+1=3x+21 \\ y=3x+21-1 \\ y=3x+20 \end{gathered}[/tex]Answer: y = 3x + 20
