chapter 3 sec. 3.7 equations of lines in the coordinate plane … · chapter 3 sec. 3.7 equations...
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Chapter 3
Sec. 3.7 Equations Of Lines In The
Coordinate Plane
and 3.8 Slopes Of Parallel
And Perpendicular Lines
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
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
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