# Question #8dc03

Jun 27, 2017

$x = - 6$

#### Explanation:

The line we are trying to find is perpendicular to $y = 5$, which is a horizontal line.

The line which is perpendicular (at ${90}^{o}$) to a horizontal line is a vertical line, which would have the equation $x = \text{number}$. SO if we were to put any line which has the general equation $x = \text{number}$, the line should be perpendicular to $y = 5$

Let's try this for $x = 9$:

As you can, the angle between the two lines is ${90}^{o}$, hence $x = 9$ is perpendicular to $y = 5$

One thing you should notice about any vertical line is that the $x$-coordinate is always the number that $x$ equals in the equation. So with $x = 9$, all the points will have an $x$-coordinate of 9.

Since we need the vertical line to go through $\left(- 6 , 1\right)$, which has $x$-coordinate $- 6$, the vertical line equation would be $x = - 6$

If we graph this, it would look like:

$x = - 6$ is perpendicular to $y = 5$ and also goes through the point $\left(- 6 , 1\right)$, so this is your answer.

All lines with the general equation $x = \text{number}$, will not intercept the $y$-axis, hence they will not have $y$-intercepts. But, as mentioned before, all points will have an $x$-coordinate of the number given, so the $x$-intercept will also be the number given. As the equation of our line is $x = - 6$, the $x$-intercept is $- 6$.