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4-7B Perpendicular Lines

Algebra 1 Glencoe McGraw-Hill Linda

Stamper

What is the reciprocal of 8?

What is the opposite reciprocal of 8?

In this lesson you will need to find and use

opposite reciprocals.

Two lines in a coordinate plane are perpendicular

if they intersect at right angles (90 degree

angles). Horizontal and vertical lines are

perpendicular to each other.

y

x

In a coordinate plane, two non vertical lines are

perpendicular if and only if the product of their

slopes is 1.

y

x

Do you think these lines are perpendicular?

How to determine whether lines are perpendicular.

1. Write each line in slope-intercept form.

2. Multiply the slopes together.

3. If the product is 1, then the lines are

perpendicular.

Write the equation of each line in the graph.

Determine whether the lines are perpendicular.

y

Blue line

Green line

y-intercept is 1

y-intercept is 3

x

These are opposite reciprocals!

The lines are perpendicular!

Example 1 Write the equation of each line in the

graph. Determine whether the lines are

perpendicular.

y

Blue line

Green line

y-intercept is 4

y-intercept is 3

x

The lines are not perpendicular!

Example 2 Write the equation of each line in the

graph. Determine whether the lines are

perpendicular.

y

Blue line

Green line

y-intercept is 1

y-intercept is 4

x

The lines are perpendicular!

Write the slope-intercept form of an equation for

the line that passes through (-4,-3) and is

perpendicular to the graph of 4x y 2.

y

Find the slope of the given line.

Find the opposite reciprocal.

x

Use slope-intercept or point-slope to write the

equation.

(-4,-3)

Write the slope-intercept form of an equation for

the line that passes through (-4,-3) and is

perpendicular to the graph of 4x y 2.

(when no graph is given)

Find the slope of the given line.

Find the opposite reciprocal.

Use slope-intercept or point-slope to write the

equation.

Example 3 Write the slope-intercept form of an

equation for the line that passes through (-3,-2)

and is perpendicular to the graph of x 4y 12.

Example 4 Write the slope-intercept form of an

equation for the line that passes through (4,7)

and is perpendicular to the graph of -2x 3y

-3.

Example 5 Write the slope-intercept form of an

equation for the line that passes through (4,-1)

and is perpendicular to the graph of 7x - 2y 3.

Find slope of given line.

Find the opposite reciprocal.

Use slope-intercept or point-slope form to write

the equation.

Example 3 Write the slope-intercept form of an

equation for the line that passes through (-3,-2)

and is perpendicular to the graph of x 4y 12.

Find slope of given line.

Use slope-intercept or point-slope form to write

the equation.

Find the opposite reciprocal.

Example 4 Write the slope-intercept form of an

equation for the line that passes through (4,7)

and is perpendicular to the graph of -2x 3y

-3.

Find slope of given line.

Use slope-intercept or point-slope form to write

the equation.

Find the opposite reciprocal.

Example 5 Write the slope-intercept form of an

equation for the line that passes through (4,-1)

and is perpendicular to the graph of 7x - 2y 3.

Find slope of given line.

Use slope-intercept or point-slope form to write

the equation.

Find the opposite reciprocal.

Write an equation in slope-intercept form for a

line perpendicular to the graph of -3x 2y 6

that passes through the x-intercept of the line.

(but no graph is given)

y

What is the problem asking you to do?

x

-3x2y6

Write equation for this line.

Write an equation in slope-intercept form for a

line perpendicular to the graph of -3x 2y 6

that passes through the x-intercept of the line.

Find slope of given line.

Find the x-intercept of the given line.

Coordinate of x-intercept is (-2,0).

Find the opposite reciprocal.

Use slope-intercept or point-slope form to write

the equation.

Write an equation in slope-intercept form for a

line perpendicular to the graph of -3x 2y 6

that passes through the x-intercept of the line.

y

x

Example 6 Write an equation in slope-intercept

form for a line perpendicular to the graph of x

3y 6 that passes through the x-intercept of the

line.

Example 7 Write an equation in slope-intercept

form for a line perpendicular to the graph of 3x

2y 8 that passes through the y-intercept of

the line.

Find slope of given line.

Find the opposite reciprocal.

Find the intercept of given line.

Use slope-intercept or point-slope form to write

the equation.

Example 6 Write an equation in slope-intercept

form for a line perpendicular to the graph of x

3y 6 that passes through the x-intercept of the

line.

Find slope of given line.

Find the x-intercept of the given line.

Coordinate of x-intercept is (6,0).

Use slope-intercept or point-slope form to write

the equation.

Find the opposite reciprocal.

Example 7 Write an equation in slope-intercept

form for a line perpendicular to the graph of 3x

2y 8 that passes through the y-intercept of

the line.

Find slope of given line.

Find the x-intercept of the given line.

Coordinate of y-intercept is (0,4).

Find the opposite reciprocal.

Use slope-intercept or point-slope form to write

the equation.

Homework

4-A15 Pages 240-241 1825,28-30,36 and Skills

Practice Wkbk. Page 30 13-24.

Review nightly for trimester 1 exam.