Slopes of Parallel and Perpendicular Lines Recall that two lines are parallel if they are in the same plane and do not intersect. Two lines are perpendicular.

Slides:

Advertisements

Similar presentations

Writing Parallel and Perpendicular Lines Part 1. Parallel Lines // (symbol) All parallel lines have the same slope. Parallel lines will NEVER CROSS. Since.

Advertisements

Parallel and Perpendicular Lines

Perpendicular Lines. ┴ Perpendicular lines are lines that intersect in a right angle. ┴ The slopes of perpendicular lines are negative reciprocals of.

Unit 1 Basics of Geometry Linear Functions.

Slope and Rate of Change Equations of Lines

Warm-Up On the same coordinate plane… ▫Graph the equation y=2x +3 ▫Graph the equation y=2x ▫Graph the equation y= - ½x + 1 What do you notice about the.

Slope MATH 018 Combined Algebra S. Rook. 2 Overview Section 3.4 in the textbook –Definition and properties of slope –Slope-intercept form of a line –Slopes.

Geometry Section 3.6 “Slope of Parallel and Perpendicular lines”

Parallel Lines Lines are parallel if they have the same slope.

Determining if Lines are Parallel or Perpendicular Parallel linesPerpendicular lines Slopes are the same Slopes are opposite reciprocals (assume no vertical.

Section 7.3 Slope of a Line.

Finding Equation of Lines Parallel and Perpendicular to Given Lines Parallel linesPerpendicular lines Slopes are the same Slopes are opposite reciprocals.

Warm Up for 9.6 Find the distance and midpointbetween the following sets of points. (5, 19) and (-3, -1) (7, -16) and (-2, -1) (1, -4) and (0, 0) (-6,

Parallel and Perpendicular Lines

It’s What’s Going On!. Recall y = mx + b is the equation of a line m is the value of the slope of a line (rise over run) b is the y-intercept m = 1 __.

Parallel and Perpendicular Lines Chap 4 Supplemental Lecture.

Geometry 3.4 Big Idea: Find the Slope of a Line. Determine if lines are parallel or perpendicular.

Review of lines Section 2-A. Slope (m) of a line Let P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) be points on a nonvertical line, L. The slope of L is.

Slopes of Equations and Lines Honors Geometry Chapter 2 Nancy Powell, 2007.

Slopes and Parallel Lines Goals: To find slopes of lines To identify parallel lines To write equations of parallel lines.

Lines: Slope The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line. As a formula, slope =

Everything You Will Ever Need To Know About Linear Equations*

3-7 Equations of Lines in the Coordinate Plane

3.4 – FIND AND USE SLOPES. Slope: measures the steepness of a line or the rate of change. Slope = m = Rise Run Up or down Left or right =

Warm Up Given: (3, -5) and (-2, 1) on a line. Find each of the following: 1.Slope of the line 2.Point-Slope equation of the line 3.Slope-Intercept equation.

Advanced Algebra Notes Section 2.2: Find Slope & Rate of Change The steepness of a line is called the lines The slope of a non-vertical line is: The slope.

Equations of Lines Standard Form: Slope Intercept Form: where m is the slope and b is the y-intercept.

2.2 Slope and Rate of Change, p. 75 x y (x1, y1)(x1, y1) (x2, y2)(x2, y2) run (x2 − x1)(x2 − x1) rise (y2 − y1)(y2 − y1) The Slope of a Line m = y 2 −

4.4 Slope of a Line. Slope – a measure of how steep a line is. Slope is the ratio of the vertical change to the horizontal change of a nonvertical line.

In your math notebook find the value of x so that the lines are parallel.

8.2 Lines and Their Slope Part 2: Slope. Slope The measure of the “steepness” of a line is called the slope of the line. – Slope is internationally referred.

Parallel/ Perpendicular Lines Section 2.4. If a line is written in “y=mx+b” form, then the slope of the line is the “m” value. If lines have the same.

WARM UP 1. Name the alternate interior angles 2. Name the alternate exterior angles 3. Name the corresponding angles.

5-6 PARALLEL AND PERPENDICULAR LINES. Graph and on the same coordinate plane. Parallel Lines: lines in the same plane that never intersect Non-vertical.

Warm up Recall the slope formula:

Write Equations of Parallel and Perpendicular Lines

Section 6.6 Parallel and Perpendicular Lines. Definitions Lines that lie in the same plane and never intersect are called parallel lines. All vertical.

Daily Homework Quiz Graph each line. - x 3 2 y = 3– 1. y = 2x2x ANSWER.

Slope Lesson 4.6.

Class Work: Algebra Parallel & Perpendicular Lines You need your notes. Title the notes: Parallel & Perpendicular Lines I will check your work at the end.

Slope of a Line. Slopes are commonly associated with mountains.

3.4 Find and use Slope of Lines. Slope Slope is: Rate of change A ratio of rise and run The change in Y over the change in X The m is Y = mX +b.

Everything You Will Ever Need To Know About Linear Equations* *Whether You Wanted To Know It Or Not!

Distance On a coordinate plane Finding the length of a line segment.

5.6 Parallel and Perpendicular Equations

2.4 – Parallel and Perpendicular Lines

1.4 Lines, writing, finding slopes and intersections Part I

Warm Up Use the figure below to answer each question

Lines: Slope The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line. As a formula, slope =

Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

Math The Slope of a Line.

Parallel Lines: SLOPES ARE THE SAME!!

Algebra 1 Review Linear Equations

2.5 Linear Equations.

TEST 1-4 REVIEW 381 Algebra.

5-6 Parallel and Perpendicular Lines

The ratio of vertical change to horizontal change

Section 3.6 Find and Use Slopes of Lines

WARM UP 1. Name the alternate interior angles

Geometry Section 3.3 Reitz High School

TEST 1-4 REVIEW 381 Algebra.

Objective: Find the slope of a line given two point

Warm Up Write the Standard Form equation of

Warm Up x – 5 = 0 Write the Standard Form equation of

Warm-Up 1.) Using the point slope formula find the equation of a line with slope -2 , passing through the point (1, 3) 2.) Graph the line y = 3x + 4.

Slope Graphing Day 2.

Presentation transcript:

Slopes of Parallel and Perpendicular Lines Recall that two lines are parallel if they are in the same plane and do not intersect. Two lines are perpendicular if they intersect at a right angle

Example 1: Consider the following graph with two lines that are parallel. Since both lines have the same “steepness”, their slopes must be the same value.

Example 2: Consider the following graph with two lines that are perpendicular. Notice that the line in red has a positive slope (rising), while the line in blue has a negative slope (falling).

This is a quite interesting result. Not only are the slopes opposite in sign, but they are reciprocals! As it turns out, this is always the case, assuming that neither line is vertical, which has undefined slope.

Example 3: Special case #1 When both lines are vertical, they are parallel. Recall that vertical lines have undefined slope. Thus, …

Example 4: Special case #2 When one line is vertical, and the other is horizontal, then the lines are perpendicular. The slope of the vertical line is undefined … … and the slope of the horizontal line is zero.

SUMMARY Parallel linesPerpendicular lines Slopes are the same Slopes are opposite reciprocals (assume no vertical lines)

a) Determine the slope of Line 2 that is parallel to Line 1 Example 5: Line 1 has a slope of – 3. b) Determine the slope of Line 3 if it is perpendicular to Line 1

a) Determine the slope of Line 2 that is parallel to Line 1 Example 6: Line 1 has a slope of 3/4.

Line 1 has a slope of 3/4. b) Determine the slope of Line 3 if it is perpendicular to Line 1

While we have written out all the details, these problems are usually done in your head. For part b again … Use two steps: 1) The reciprocal is: 2) Take the opposite: