# What is the equation of the line perpendicular to y - 4 = 0 and passing through (-1, 6)? Please show working.

Mar 22, 2018

$x = - 1$

#### Explanation:

$\text{note that "y-4=0" can be expressed as } y = 4$

$\text{This is a horizontal line parallel to the x-axis passing }$
$\text{through all points in the plane with a y-coordinate } = 4$

$\text{A line perpendicular to "y=4" must therefore be a }$
$\text{vertical line parallel to the y-axis}$

$\text{such a line has equation "x=c" where c is the value}$

$\text{of the x-coordinate the line passes through}$

$\text{here the line passes through } \left(- 1 , 6\right)$

$\text{the equation of the perpendicular line is therefore}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{x = - 1} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
graph{(y-0.001x-4)(y-1000x-1000)=0 [-10, 10, -5, 5]}