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 of parallel and perpendicular lines and how slopes are related. Find the equation of a line perpendicular to a given line through a given point. Warm Up Review Notes – Parallel lines Practice Review Homework – Page 574 problems 55, 58, 59, and 60 all

Warm Up Write the equation in point-slope form for the line that passes through the given points a. (3, 3) and (4, 5) b. (0, 0) and (4, 6) c.(1, 3) and (2, 1) Homework – Page 574 problems 55, 58, 59, and 60 all

Parallel Lines Parallel Lines – two or more lines in the same plane that never intersect Slopes of Parallel Lines Nonvertical lines are parallel if they have the same slope and different y-intercepts. Slopes of Parallel Lines Any two vertical lines are parallel

Determining Whether Lines are Parallel EXAMPLE 1 2x + 6y = 12 6y = –2x + 12 –2x 6 6 y = – x

Writing Equations of parallel lines EXAMPLE 2 Write the equation in slope-intercept form of the line that contains (5, 1) and is parallel to y = 3x – 2. Step 1 – Identify the slope of the given line m = 3For parallel lines slopes are equal Step 2 – Write the equation in slope-intercept form y – y 1 = m(x – x 1 ) y – 1 = 3(x – 5) y – 1 = 3x – 15 y = 3x – 14 Write in point-slope form Use distributive property Add 1 to both sides

You try one Write the equation of the line parallel to y = 2x + 1 and contains (–3, –4)

Class work – Please do these now Page 262 problems 2 to 18 even Homework – Please do at home tonight Page 574 problems 55, 58, 59, and 60 all

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 of parallel and perpendicular lines and how slopes are related. Find the equation of a line perpendicular to a given line through a given point. Warm Up Review Notes – Perpendicular lines Practice Review Homework – Page 574 problems 56 and 57 all

Warm Up Write the equation for the line parallel to the given line and that passes through the given point a. 2x – 2y = 6 and (3, 4) b. y = 3x – 5 and (0, 3) c. y = 5 and (1, 3) Homework – Page 574 problems 56 and 57 all

Perpendicular Lines Perpendicular Lines – two lines intersect to form a right angles. Slopes of Perpendicular Lines Two lines are perpendicular if the product of their slopes equals –1. Slopes of Perpendicular Lines A vertical and horizontal line are also perpendicular

Writing Equations for Perpendicular Lines EXAMPLE 3 Write the equation in slope-intercept form of the line that contains (3, 1) and is perpendicular to y = 0.5x – 2. Step 1 – Identify the slope of the given line m = 0.5 Negative reciprocal of 0.5 is –2 Step 3 – Write the equation in slope-intercept form y – y 1 = m(x – x 1 ) y – 1 = –2(x – 3) y – 1 = –2x + 6 y = –2x + 7 Write in point-slope form Use distributive property Add 1 to both sides Step 2 – Find the negative reciprocal of the slope m = –2

Applications EXAMPLE 4 Step 1 Find the slope of Park Road: Step 2 Find the negative reciprocal of the slope A Jogging path for a new city park will connect the park entrance to Park Road. The path will be perpendicular to Park Road. Write an equation for the line representing the jogging path y 2 – y 1 x 2 – x 1 m = 5 – 1 4 – 2 = = 2 Step 3 Write the equation in slope-intercept form The slope is 2 so the negative reciprocal is – 1212 y = – x

Class work – Please do these now Pages 262/263 problems 20 to 46 even Homework – Please do at home tonight Page 574 problems 56 and 57 all