Chapter 3

Sec. 3.7 Equations Of Lines In The

Coordinate Plane

and 3.8 Slopes Of Parallel

And Perpendicular Lines

Review

Lesson Purpose

• Objective

• Write an equation of a

line given

characteristics of

parallel or

perpendicular lines.

• Essential Question

• How can you prove

that two lines are

parallel?

Point-Slope Form-

• is an equation of a line with a point on a line,

(x₁, y₁) is

• y- y₁=m(x- x₁) where

• y₁= y₁-coordinate

• m=slope

• x₁= x₁-coordinate

Key Concepts

Slope- Intercept form

• y= mx + b

• ↑ ↑

• slope y-intercept

• ↓ ↓

• y= 3x + 8

Point-Slope Form

• y - y₁=m (x - x₁)

• (x₁, y₁)= point on line

• m= slope

• y-5 = -2(x-3)

Example #1 :Slope with y-intercept

Write an equation in slope intercept form of the line with

slope 6 and y-intercept of -3. Then graph the line

• y=mx +b

6 rise

1 run

Questions #1

A. y=¾x -5

B. y=-¾x+5

C. y=5x+¾

D. y=-5x-¾

• What is the equation of the line with a slope -¾ and y-

intercept 5?

Questions #2

• What is the equation of the line with a slope 2 and y-

intercept 4?

A. y=2x -4

B. y=4x+2

C. y=2x+4

D. y=4x-2

Example #2: slope with a point

Write an equation in point-slope form of the line with

slope= -3/5 that contains (-10,8) Then graph the

line.

• y - y₁=m (x - x₁)

• Substitute into equation

-3 down

5 run

Question #3

• A. y+4 = -3(x-1)

• B. y-4 = 3(x+1)

• C. y+4 = 3(x-1)

• D. y-4 = -3(x+1)

• Write an equation in point-slope form of the line with slope= -3 that contains (-1,4) Then graph the line.

Question #4

• Write an equation in slope intercept form of the line with

slope= -3 that contains (-1,4) Then graph the line.

• A. y= -3x-1

• B. y= 3x+1

• C. y=-3x+5

• D. y= 3x-5

Example #3 Two Points

• Write an equation of the line through each pair of points in

slope intercept form. (4, 9) and (-2,0)

• Step 1: use slope equation:

Question #5

• Write an equation of the line through each pair of points in

slope intercept form. (-2, -1) and (3,5)

• A. y= 6/5x+7/5

• B. y=-6/5x+7/5

• C. y=7/5x+6/5

• D. y=-7/5x+6/5

Question #6

• Write an equation of the line through each pair of points in

slope intercept form. (1, 1) and (2,-4)

• A. y= 1/2x+3

• B. y=-1/2x+5

• C. y=1/2x-5

• D. y=-1/2x+3

Horizontal and Vertical Line

Horizontal Equation

• y= b like y=2

• b= y-intercept

• Is on the y axis

Vertical Line

• x= a like x= 4

• a= x-intercept

• Is on x axis

• Parallel lines have the same slope.

3.8 Slopes of Parallel lines

Example #4 Writing Parallel Equations Of A Line

• Write an equation in slope-intercept form for a line

parallel to y=3x +5 containing points (3,-4)

Question # 7

• Write an equation for the line parallel to the given line

that contains point C.

• ;C(4, 3)

• A. y=½x +5

• B. y =½x-1

• C. y=-2x+1

• D. y=-2x-5

14

2y x

• Write an equation for the line parallel to the given line

that contains point C. y = 2x 4; C(3, 3)

• A. y=-½x +9

• B. y =-½x-3

• C. y=-2x+9

• D. y=-2x+3

Question # 8

• The product of the slopes of two perpendicular lines is -1

or the slopes are negative reciprocal.

• Product means multiplication.

Slopes of Perpendicular Lines

Example #5 Writing Perpendicular Equations Of A

Line

• Write an equation in slope-intercept form for a

line perpendicular to y=3x +5 containing points

(3,-4)

Question #9

• Write an equation of the line perpendicular to the

given line that contains P, P(4, 3); y = ¼x 15.

• A. y=4x +13

• B. y =4x-13

• C. y=-4x+19

• D. y=-4x-19

Question #10

• Write an equation of the line perpendicular to the

given line that contains P, P(6, 5); y = 2x 3

• A. y=-½x +2

• B. y =-½x-8

• C. y=-½x+8

• D. y=-½x-2

Ticket Out and Homework

Ticket Out

• How can you tell if the

lines are parallel or

perpendicular?

Homework

• Sec. 3.7 Part B: pg 211

#’s 4,5,7,8, 15, 16, 17

• Sec 3.8 Pg 216 #’s 7,8,

9,11,12, 14,15, 16,17, 19