# How do you find the slope of the line parallel to and perpendicular to y=x+3?

Aug 26, 2017

See a solution process below:

#### Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

$y = x + \textcolor{b l u e}{3}$

or

$y = \textcolor{red}{1} x + \textcolor{b l u e}{3}$

Therefore the slope of the line is: $\textcolor{red}{m = 1}$

Parallel Lines

Parallel lines by definition have the same slope. Therefore, the slope of a line parallel to the line in the problem will be:

$\textcolor{red}{m = 1}$

Perpendicular Lines

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

The formula for the slope of a perpendicular line is:

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

Substituting gives:

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