AgendaLesson 5-5 – Parallel and Perpendicular Lines

Standards7.0 Derive linear equations by using the point-slope formula8.0 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 UpReview

Notes – Parallel linesPracticeReview

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 LinesNonvertical lines are parallel if they have the same slope and different y-intercepts.

Slopes of Parallel LinesAny two vertical lines are parallel

Determining Whether Lines are ParallelEXAMPLE 1

2x + 6y = 12

6y = –2x + 12

–2x –2x

6 6

y = – x + 21

3

Writing Equations of parallel linesEXAMPLE 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 = 3 For parallel lines slopes are equal

Step 2 – Write the equation in slope-intercept form

y – y1 = m(x – x1)

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 nowPage 262 problems 2 to 18 even

Homework – Please do at home tonight Page 574 problems 55, 58, 59, and 60 all

AgendaLesson 5-5 – Parallel and Perpendicular Lines

Standards7.0 Derive linear equations by using the point-slope formula8.0 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 UpReview

Notes – Perpendicular linesPracticeReview

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 LinesTwo lines are perpendicular if the product of their slopes equals –1.

Slopes of Perpendicular LinesA vertical and horizontal line are also perpendicular

Writing Equations for Perpendicular LinesEXAMPLE 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 – y1 = m(x – x1)

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

ApplicationsEXAMPLE 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

y2 – y1

x2 – x1

m = 5 – 1

4 – 2 = = 2

Step 3 Write the equation in slope-intercept form

The slope is 2 so the negative reciprocal is –

1

2

y = – x + 41

2

Class work – Please do these nowPages 262/263 problems 20 to 46 even

Homework – Please do at home tonight Page 574 problems 56 and 57 all