This document provides background information and examples on parallel and perpendicular lines. It discusses how to identify the slope of a line from its equation in slope-intercept or standard form. It notes that parallel lines have the same slope, while perpendicular lines have slopes that are opposite reciprocals whose product is -1. Examples are provided to find the slopes of parallel and perpendicular lines and to write equations of lines given a point and slope.

1. Parallel & Perpendicular Lines Section 5.8

2. Background: Slope If a line is in slope intercept form the slope is easy to locate. Where is the slope located in slope- intercept form? What is the slope of an equation of x= ? What is the slope of an equation of y= ?

3. Background: Slope Standard Form Let’s transform Standard Form into Slope-Intercept Form Ax + By = C By = -Ax + C y = - A/B x + C/B What’s the slope? m = -A/B

4. Ex 1a: Parallel Lines The slope of parallel lines are exactly the same. All horizontal lines are parallel and have a slope of what? All vertical lines are parallel and have a slope of what? Regardless of the form of the equation, you just have to find the slope and you have the slope of all the parallel lines.

5. Ex 1b: Parallel Lines In these equations, you will be given an equation and a point. Find the slope of the equation. (That’s all you need the equation for. You are now finished with it.) Now, use the slope and the point to find the y-intercept. Plug the slope and the y intercept into the equation.

6. Ex 2: Perpendicular Lines Perpendicular lines form right angles when they meet. The slopes of perpendicular lines are opposite reciprocals. When you multiply perpendicular slopes together, their products equal -1.

7. Ex 2: Perpendicular Lines Examples of opposite reciprocals: 1/3 and -3/1 1 and -1 -1/2 and 2/1 What is the opposite reciprocal of -3/5? 5/3

8. Review