Parallel and Perpendicular Lines

Lesson 5.5

Alg 7.0Derive linear equations by using the point-slope formula.

Alg 8.0Understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Find the equation of a line perpendicular to a given line that passes through a given point.

Lesson Objective: Students will be able to write equations of parallel and perpendicular lines as demonstrated by a Ticket out the Door.

Graph the following on the coordinate plane.

y x 1

23 y x

1

21

m1

2b 3

m1

2b 1

x

y

Parallel lines have the same slope.

Parallel linesTwo lines are parallel if they never intersect.

Example:

Parallel lines Not parallel lines

What do we know about the slope of parallel lines?

Think Pair Share:

Graph the following on the coordinate plane.

x

yy x

2

31 y x

3

24

m2

3

b 1

m 32

b 4

Lines appearperpendicular

Perpendicular lines have slopes that are opposite reciprocals

Perpendicular LinesTwo lines are perpendicular if they intersect to form right angles.

Example:

Perpendicular Not perpendicular

What do we know about the slope of perpendicular lines?

Lines are perpendicular if the product of the slopes is -1 (opposite and reciprocal).

Think Pair Share:

I Do!Find the slope only of a line parallel and perpendicular to the graph of each equation.

y 2

3x 1

Example 1: m=2

Example 2:

We Do!Find the slope of a line parallel and perpendicular to the graph of each equation.

)2(43 xy

We Do!Find the slope of a line parallel and perpendicular to the graph of each equation.

Think Pair Share:

3x 4y 12

You Do!Find the slope of a line parallel and perpendicular to the graph of each equation.

22 yx

7x y 5

Partner A on the White Board

Partner B on the White Board

Determine if the lines in each pair are parallel or perpendicular?

823 yx22

3 xy

Part 1: Parallel Lines

Parallel lines:Lines are parallel if they have the same slope but different y-intercepts.

Write in slope-intercept form the equation of the line that is parallel to the line in the graph and passes through the given point.

Step 1:Determine

the slope that you will need

m =

Step 2: take the given point

x1 =

y1 =

Step 3: plug the point and slope into the point - slope formula

y – y1 = m(x – x1)

Flow map for parallel lines:

Point-Slope Form

Step 4: distribute and solve for “y”

y = mx + b

Slope-Intercept Form

Stop here if the question asks for Point Slope Form

Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (6, 2).

I Do!

53 xy

We Do!

Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (-4, -6).

62 xy

You Do!Partner A on the Whiteboard:Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (0,1).

26 xy

You Do!Partner B on the Whiteboard:Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (-3,5).

32 xy

Part 2: Perpendicular Lines

Perpendicular linesLines are perpendicular if the product of their slopes equals −1

The slopes are:*opposite *reciprocal

Write in slope-intercept form the equation of the line that is perpendicular to the line in the graph and passes through the given point.

I Do!Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (6, 2).

53 xy

We Do!Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (0, 1).

72 xy

You Do! Partner A on the Whiteboard

Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (-1, 2).

3xy

Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (-1, -2).

You Do! Partner B on the Whiteboard

24

1 xy

Summary

• Parallel Lines: They have the same exact slope (m) and different y-intercepts (b)

• Perpendicular Lines: Their slopes are opposite (change the sign) and reciprocals (flip)of each other.