# How do you find the slope that is perpendicular to the line -15 +3y = -12x?

Nov 23, 2017

See a solution process below:

#### Explanation:

First, we need to find the slope of the line in the problem. We can transform this equation into 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

$- 15 + \textcolor{red}{15} + \textcolor{b l u e}{12 x} + 3 y = \textcolor{b l u e}{12 x} - 12 x + \textcolor{red}{15}$

$0 + 12 x + 3 y = 0 + 15$

$12 x + 3 y = 15$

$\frac{12 x + 3 y}{\textcolor{red}{3}} = \frac{15}{\textcolor{red}{3}}$

$\frac{12 x}{\textcolor{red}{3}} + \frac{3 y}{\textcolor{red}{3}} = 5$

$\textcolor{red}{4} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{15}$

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

Therefore, the slope of the line in the problem is:

$m = - \frac{\textcolor{red}{4}}{\textcolor{b l u e}{1}} = - 4$

Let's call the slope of a perpendicular line: ${m}_{p}$

The slope of a perpendicular line is the negative inverse of the slope of the line it is perpendicular to.:

${m}_{p} = - \frac{1}{m}$

Substituting gives:

${m}_{p} = - \frac{1}{-} 4 = \frac{1}{4}$