Download Chapter 4.9(b) Slopes of Parallel and Perpendicular Lines.notebook

Chapter 4.9(b) Slopes of Parallel and Perpendicular Lines.notebook
Bellwork:
November 10, 2016
Homework Questions???
Solve
1)
2)
Write the equation of the line described.
3) Parallel to y = ­x ­ 4; through (­3, ­2)
Nov 4­9:34 AM
Nov 4­10:22 AM
Graph the following equations on the same coordinate plane.
y = 2x ­ 4
Chapter 4.9(b) Slopes of Parallel and Perpendicular Lines
y = ­½x + 1
Identify lines that are perpendicular and write equations to describe lines perpendicular to a given line.
What do you notice about the lines?
Will they ever intersect?
What are there slopes?
Nov 4­10:22 AM
Nov 7­4:29 PM
Identify which lines are perpendicular:
1)
Perpendicular Lines: Lines that intersect to form a right angle (90O).
Two non­vertical lines are perpendicular if and only if the product of their slopes is ­1 (opposite reciprocals).
2) Vertical lines are perpendicular to horizontal lines.
Nov 7­4:30 PM
Nov 7­4:30 PM
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Chapter 4.9(b) Slopes of Parallel and Perpendicular Lines.notebook
Perpendicular lines can be used to show if a figure has one or more right angles.
November 10, 2016
Finding slopes of perpendicular lines:
4) Identify the slope of a line perpendicular to the line described by y = ¾x + 2.
3) Is triangle ABC a right triangle?
B(1, 2)
Find the slopes of the lines and compare.
A(­2, 0)
5) Identify the slope of a line perpendicular to the line described by ­2x + 4y = 12.
C(0, ­3)
Nov 7­4:30 PM
Nov 4­4:12 PM
We can use slope to write an equation of a line perpendicular to a given line.
Graph the line y = 3x + 5
Example: Write an equation for the line that contains the point (2, ­1) and is perpendicular to the graph of y = 2x ­ 5
Step 1: Find slope of the given equation by solving for y.
Graph a line perpendicular to the above line through the point (2, 3)
m = Step 2: Write the equation in point­slope form
m = ­½
(2, ­1)
Write the equation of the line you just drew.
y ­ (­1) = ­½(x ­ (2))
y + 1 = ­½(x ­ 2)
Step 3: Write the equation in slope intercept form.
y + 1 = ­½(x ­ 2)
y + 1 = ­½x + 1
­1
­1
y = ­½x Nov 7­4:36 PM
Nov 4­4:27 PM
Write the equation in slope­intercept form for the line that is perpendicular to the given line and passes through the given point.
6) 5x ­ 2y = 8; (­5, 2)
The slopes of parallel lines are ______________.
The slopes of perpendicular lines are __________
______________.
7) 4x + 8y = 12; (­3, ­5)
Nov 4­4:32 PM
Nov 4­4:11 PM
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Chapter 4.9(b) Slopes of Parallel and Perpendicular Lines.notebook
November 10, 2016
Homework
P. 297­299 #5­7, 13­16, 34­45 (all)
Nov 4­4:34 PM
Nov 4­4:35 PM
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