Write Equations of Parallel and Perpendicular lines Section 5.5 #37 "Arithmetic is being able to count up to twenty without taking off your shoes." -- Mickey Mouse
The Concept In Chapter 4 we learned that parallel lines have slopes that are equal but have different y-intercepts In Chapter 4 we learned that parallel lines have slopes that are equal but have different y-intercepts Today we’re going to learn about writing parallel line equations and also about perpendicular lines Today we’re going to learn about writing parallel line equations and also about perpendicular lines In order to work through today’s lesson, we’ll be drawing heavily on our work with writing equations in slope intercept form In order to work through today’s lesson, we’ll be drawing heavily on our work with writing equations in slope intercept form
Parallel Lines In Chapter 4 we discussed the concept that lines that have the same slope but different y-intercepts In Chapter 4 we discussed the concept that lines that have the same slope but different y-intercepts Based on this rule, if we are asked to write an equation for a line parallel to another line, we simply “steal” it’s slope Based on this rule, if we are asked to write an equation for a line parallel to another line, we simply “steal” it’s slope For example if we wanted to write an equation for a line that goes through the point (-3,3) and is parallel to the line y=-2x+1 For example if we wanted to write an equation for a line that goes through the point (-3,3) and is parallel to the line y=-2x+1
Practice What is the equation of the line parallel to the one given and goes through the listed point
Practice
Practice
PerpendicularPerpendicular lines Perpendicular In order to understand perpendicular lines, we must first analyze the relationship between their slopes In order to understand perpendicular lines, we must first analyze the relationship between their slopes m=-1 m=2 m=-1/2 m=1
Practice Please give the slope of a line and perpendicular to the given line
Practice
Practice
Practice
Perpendicular Lines Now that we’ve established that the slopes of perpendicular lines are negative reciprocals of each other, if we are asked to write an equation for a line parallel to another line, we simply “steal” it’s slope and modify itNow that we’ve established that the slopes of perpendicular lines are negative reciprocals of each other, if we are asked to write an equation for a line parallel to another line, we simply “steal” it’s slope and modify it For example if we wanted to write an equation for a line that goes through the point (-4,3) and is perpendicular to the line y=-2x-3 For example if we wanted to write an equation for a line that goes through the point (-4,3) and is perpendicular to the line y=-2x-3
Practice What is the equation of the line perpendicular to the one given and goes through the listed point
Practice
Practice What is the equation of the line parallel to the one given and goes through the listed point
Most Important Points What’s the most important thing that we can learn from today? Two lines are parallel if they have the same slope but with different y- intercepts Perpendicular lines have slopes that are the negative reciprocals of each other
Bellwork Solution Are these two lines parallel? Be prepared to Explain Are these two lines parallel? Be prepared to Explain y-2=2x & 2x+y=7 y-2=2x & 2x+y=7 m=2 m=-2
Bellwork Solution Are these two lines parallel? Be prepared to Explain Are these two lines parallel? Be prepared to Explain -x=y+4 & 3x+3y=5 -x=y+4 & 3x+3y=5 m=-1
Homework 5.5 Exercises 1-8, 12-22, 27, 28, 32-34, 36, 38-42
Practical Example
Definitions Perpendicular Perpendicular Two lines that intersect at a 90 degree angle Two lines that intersect at a 90 degree angle