Parallel and Perpendicular Lines

Slides:



Advertisements
Similar presentations
§ 2.4 The Slope of a Line.
Advertisements

Graphing Parallel and Perpendicular Lines
Parallel & Perpendicular Lines
Parallel and Perpendicular Lines
7.8 Parallel and Perpendicular Lines Standard 8.0: Understand the concepts of parallel and perpendicular lines and how their slopes are related.
Lesson 6.5 Parallel and Perpendicular Lines
4.4 Parallel and Perpendicular Lines
1.4: equations of lines CCSS:
5.7 Parallel and Perpendicular Lines
Agenda Lesson 5-5 – Parallel and Perpendicular Lines Standards 7.0 Derive linear equations by using the point-slope formula 8.0 Understand the concept.
Chapter 3 Introduction to Graphing and Equations of Lines
Parallel & Perpendicular Lines
2.5 The Point-Slope Form of the Equation of a Line.
Writing equations given slope and point
Bellwork Partner Activity for graphing.
Parallel Lines Lines are parallel if they have the same slope.
CONCEPT: WRITING EQUATIONS OF LINES EQ: HOW DO WE WRITE THE EQUATION OF A LINE THAT IS PARALLEL OR PERPENDICULAR TO A GIVEN LINE? (G.GPE.5) VOCABULARY.
Write an equation given the slope and a point EXAMPLE 2 Write an equation of the line that passes through (5, 4) and has a slope of –3. Because you know.
4.7 Graphing Lines Using Slope Intercept Form
2.5 Linear Equations. Graphing using table Graphing using slope and y-intercept (section 2.4) Graphing using x-intercept and y-intercept (section 2.5)
Linear Equations in Two Variables
7.2 Review of Equations of Lines; Linear Models
Equations of lines.
Warm Up Identify which lines are parallel.
EXAMPLE 1 Write an equation of a line from a graph
Copyright © Cengage Learning. All rights reserved. 1.1 Lines in the Plane.
Parallel and Perpendicular Lines Chap 4 Supplemental Lecture.
Goal: Write a linear equation..  1. Given the equation of the line 2x – 5y = 15, solve the equation for y and identify the slope of the line.  2. What.
Section 1.1 Slopes and Equations of Lines
Day Problems Graph each equation.
Parallel and Perpendicular lines I can write an equation of a line that passes through a given point, either parallel or perpendicular to a given line.
Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula.
Writing & Identifying Equations of Parallel & Perpendicular Lines Day 94 Learning Target: Students can prove the slope criteria for parallel and perpendicular.
3-7 Equations of Lines in the Coordinate Plane
C ollege A lgebra Linear and Quadratic Functions (Chapter2) 1.
Writing Equations of a Line. Various Forms of an Equation of a Line. Slope-Intercept Form.
 Parallel Lines = Lines in the same plane that never intersect.  Review:  Slope-Intercept form: y = mx+b.
2.4 Essential Questions What is the point-slope form?
§ 2.5 Equations of Lines. Martin-Gay, Intermediate Algebra: A Graphing Approach, 4ed 22 Slope-Intercept Form of a line y = mx + b has a slope of m and.
Lesson 5.5 OBJ: To write equations of parallel and perpendicular lines.
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.
Mrs. Rivas Find the slope of the line passing through the given points.
Point-Slope Form The line with slope m passing through the point (x1, y1) has an equation the point –slope form of the equation of a line.
GEOMETRY HELP Find and compare the slopes of the lines. Each line has slope –1. The y-intercepts are 3 and –7. The lines have the same slope and different.
Algebra 1 Notes Lesson 5-6: Parallel and Perpendicular Lines.
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.
Lines in the Coordinate Plane
Parallel & Perpendicular Lines
Warm-Up 5 minutes 1. Graph the line y = 3x + 4.
Warm up Recall the slope formula:
I can determine when lines are parallel and write equations of parallel lines.
Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel Determine whether lines are perpendicular Write equations.
Section 6.6 Parallel and Perpendicular Lines. Definitions Lines that lie in the same plane and never intersect are called parallel lines. All vertical.
Splash Screen. Then/Now You wrote equations in point-slope form. Write an equation of the line that passes through a given point, parallel to a given.
Parallel and Perpendicular Lines Honors Math – Grade 8.
Slopes of Parallel and Perpendicular Lines. Different Forms of a Linear Equation  Standard Form  Slope-Intercept Form  Point-Slope Form  Standard.
Drill #23 Determine the value of r so that a line through the points has the given slope: 1. ( r , -1 ) , ( 2 , r ) m = 2 Identify the three forms (Point.
Parallel and Perpendicular Lines Section 5-6. Goals Goal To determine whether lines are parallel, perpendicular, or neither. To write linear equations.
Slope of a Line. Slopes are commonly associated with mountains.
Writing Equations of Parallel Lines (IN REVIEW) You can use the slope m of a nonvertical line to write an equation of the line in slope-intercept form.
POINTS AND LINES ON THE COORDINATE PLANE
Parallel and Perpendicular Lines
PARALLEL LINES Graphs: Lines Never Intersect and are in the same plane
Objectives Identify and graph parallel and perpendicular lines.
5-5 Parallel and Perpendicular Lines
PARALLEL LINES Graphs: Lines Never Intersect and are in the same plane
Warm up Write an equation given the following information.
Warm up Write an equation given the following info:
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.
Warm up (10/22/14) Write an equation given the following info:
Presentation transcript:

Parallel and Perpendicular Lines Using parallelism and perpendicularity to solve problems

In the graph below, the two lines are parallel In the graph below, the two lines are parallel. Parallel lines - are lines in the same plane that never intersect. The equation of line 1 is y = 2x + 1. the equation of line 2 is y = 2x -2 Slopes of Parallel Lines Nonvertical lines are parallel if they have the same slope and different y-intercepts. Any two vertical lines are parallel. Any two horizontal lines are parallel

You can use slope-intercept form of an equation to determine whether lines are parallel. Are the graphs of y = -1/3x + 5 and 2x + 6y = 12 parallel? Explain. 2x + 6y = 12 6y = -2x + 12 6y = - 2x + 12 6 y = - 1/3x + 2 Compare to y = -1/3x + 5 The lines are parallel. The equations have the same slope, -1/3, and different y-intercepts. Write 2x + 6y = 12 in slope-intercept form, then compare with y = -1/3x + 5

Are the graphs of -6x + 8y = -24 and y = 3/4x – 7 parallel? Explain.

You can use the fact that the slopes of parallel lines are the same to write the equation of a line parallel to a given line. To write the equation, you use the slope of the given line and the point-slope form of a linear equation. Step 1 Identify the slope of the given line. y = 3/5x – 4 Step 2 Write the equation of the line through (5, 1) using point-slope form. y – y1 = m(x – x1) point-slope form. y – 1 = 3/5(x – 5) Substitute (5, 1) for (x1,Y1) and 3/5 for m. y – 1 = 3/5x – 3/5(5) Use the distributive property. y – 1 = 3/5x – 3 Simplify. y = 3/5x – 2 Add 1 to each side. TRY ONE

Write an equation for the line that contains (2, -6) and is parallel to y = 3x + 9 Step 1 Identify the slope of the given line. Step 2 Write the equation of the line through (2, -6) using point-slope form of a linear equation. y – y1 = m(x – x1)

Write an equation for the line that is parallel to the given line and that passes through the given point. Y = 6x - 2; (0, 0) Y = -3x; (3, 0) Y =-2x + 3; (-3, 5) Y = -7/2x + 6; (-4, -6)

The two lines in the graph below are perpendicular The two lines in the graph below are perpendicular. Perpendicular lines – are lines that intersect to form right angles. The line y = 2x + 1 is perpendicular to the line y = -1/2x + 1. Slopes of perpendicular lines Two lines are perpendicular if the product of their slopes is -1. A vertical and a horizontal line are also perpendicular.

The product of two numbers is -1 if one number is the negative reciprocal of the other. Here is how to find the negative reciprocal of a number. Start with a fraction: -1/2 Find its reciprocal: -2/1 Write the negative reciprocal: 2/1 or 2 Since -1/2 • 2/1 = -1, 2/1 is the negative reciprocal of -1/2 TRY THESE

Find the negative reciprocal of each: 1) 4 2) 3/4 3) -1/2 4) -2 5) -4/3

y + 2 = -1/5x – 0 Use the distributive property. You can use the negative reciprocal of the slope of a given line to write an equation of a line perpendicular to that line. To write the equation, you use the negative reciprocal of the slope of the given line and the point-slope form of a linear equation. Step 1 Identify the slope of the given line. y = 5x + 3 Step 2 Find the negative reciprocal of the slope. 5 • -1/5 = -1 Step 3 Use the point-slope form to write an equation that contains (0, -2) and is perpendicular to y = 5x + 3 y – y1 = m(x – x1) Point-slope form. y – (-2) = -1/5(x – 0) Substitute (0, -2) for (x1,y1) and -1/5 for m. y + 2 = -1/5x – 0 Use the distributive property. y = -1/5x – 2 Subtract 2 from each side. Simplify. TRY ONE

Write an equation of the line that contains (6, 2) and is perpendicular to y = -2x + 7 Step 1 Identify the slope of the given line. Step 2 Find the negative reciprocal of the slope. Step 3 Use the point-slope form of an equation that contains (6, 2) and is perpendicular to y = -2x + 7

Write an equation for the line that is perpendicular to the given line and that passes through the given point. Y = 2x + 7; (0, 0) Y = -1/3x + 2; (4, 2) Y = x – 3; (4, 6) 4x – 2y = 9; (8, 2)

Write the equation of each line Write the equation of each line. Determine if the lines are parallel or perpendicular. Explain why or why not. Problem Solving

Problem Solving A city’s civil engineer is planning a new parking garage and a new street. The new street will go from the entrance of the parking garage to Handel St. It will be perpendicular to Handel St. What is the equation of the line representing the new street? Entrance Handel St.