# How do you find the slope that is perpendicular to the line  9x-y=9?

May 24, 2018

Slope of line, perpendicular to the line, $9 x - y = 9$ is
$- \frac{1}{9}$.

#### Explanation:

Slope of the line,  9 x -y = 9 or y= 9 x - 9 ; [y=mx+c]

is ${m}_{1} = 9$ [Compared with slope-intercept form of equation]

The product of slopes of the perpendicular lines is ${m}_{1} \cdot {m}_{2} = - 1$

$\therefore {m}_{2} = \frac{- 1}{9} = - \frac{1}{9}$. Therefore slope of the line, perpendicular

to the line, $9 x - y = 9$ is $- \frac{1}{9}$ [Ans]

May 24, 2018

See a solution process below:

#### Explanation:

This equation is in Standard Linear Form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

$\textcolor{red}{9} x - y = \textcolor{g r e e n}{9}$

$\textcolor{red}{9} x + \textcolor{b l u e}{- 1} y = \textcolor{g r e e n}{9}$

Therefore, the slope for this line is:

$m = \frac{- \textcolor{red}{9}}{\textcolor{b l u e}{- 1}} = 9$

Let's call the slope of a perpendicular line: $\textcolor{b l u e}{{m}_{p}}$

The slope of a line perpendicular to a line with slope $\textcolor{red}{m}$ is the negative inverse, or:

$\textcolor{b l u e}{{m}_{p}} = - \frac{1}{\textcolor{red}{m}}$

Substituting the slope for the line in the problem gives:

$\textcolor{b l u e}{{m}_{p}} = \frac{- 1}{\textcolor{red}{9}} = - \frac{1}{9}$