Download Lesson 13 - Writing Equations of Perpendicular Broden

LO
SWBAT write the equation of a
line that contains a given
point and is perpendicular to a
given line. A.2(F)
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DOL
Given 4 equations or graphs,
students will identify the
perpendicular slope or write
equations of perpendicular lines
correctly at least 3 times.
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Warm Up – Wednesday 10/28
1. The line to the right is shifted up 4 units.
What is the equation of the resulting line
written in the form y = mx + b?
2. Which line is parallel to 3y + 2x = 12?
A. 6x – 4y = 24
C. 2x + 3y = 6
B. y + 3x = -2
D. y = -2x + 6
3. Can parallel lines have the same y-intercept? Explain why or
why not.
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This Week:
• HW Due Tomorrow
 Make sure to SHOW WORK
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Tutoring This Week
Morning
(8:05 – 8:40 AM)
Afternoon
(4:15 – 4:45 PM)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Saturday School
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Today’s Goal:
SWBAT write the equation of a
line that contains given point
and is perpendicular to a given
line. A.2(F)
Our Goals This Week:
Be Good Citizens 100%
Exit ticket
70%
HW
90%
Why This Matters
Perpendicular lines are a part of every
day. They are present in something as
simple as certain letters of the alphabet
to the streets and buildings we encounter
in our everyday travel.
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Parallel Lines
• Never intersect
• Have the same slope
• Notation: l1 || l2
y = 3x + 5
y = 3x – 7
y = 3x + 0.5
y = 3x
l1
ALL of these lines are
parallel.
l2
They all have the
SAME slope(m).
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Perpendicular Lines
• Lines that intersect at right angles.
• Lines that have slopes that are opposite reciprocals
of each other. (sometimes called negative reciprocals)
• The product of the two slopes equals -1.
• Symbolic Notation: l1
l2
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Where do you see Perpendicular Lines in everyday life?
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Quick Check – Partner Talk
With a partner, the person who is the
younger of the two will explain the
properties of parallel lines and the other
person will explain the properties of
perpendicular lines.
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Perpendicular
Right Angels
1
2
4
3
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Negative opposite
Product
This is how you test the slope
+
–
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So What does OPPOSITE RECIPROCALS mean?
The term Opposite Reciprocals refers to two numbers that have
different signs and are flipped fractions of each other.
5
1
−3
7
5
−
1
3
7
1
−
5
7
3
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Check Yourself!
The product of the slopes of perpendicular lines is always -1!
5
1
3
−
7


1
−5
− =
5
5
−21
7
=
21
3
= -1
= -1
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Now You Try
1
6
6
−
1
5
−
8
8
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Don’t forget
to check the
products of
the slopes.
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Quick Check
On your whiteboards, create one positive and
one negative fraction and show the
opposite reciprocal of each one.
You MAY NOT use one that we have already done!
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Compare the Slopes
Find the rate of change of AB.
𝟒
𝑦
𝑟𝑖𝑠𝑒
Rate of change =
=
=
𝑥
𝑟𝑢𝑛
𝟏
4
4
-1
1
Find the rate of change of CD.
−𝟏
𝑦
𝑟𝑖𝑠𝑒
Rate of change =
=
=
𝑥
𝑟𝑢𝑛
𝟒
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Perpendicular…
These lines are parallel.
Why?
Because their slopes are
opposite reciprocals of each
other.
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Compare the Slopes
Find the rate of change of AB.
𝟑
𝑦
𝑟𝑖𝑠𝑒
Rate of change =
=
=
𝑥
𝑟𝑢𝑛
𝟐
2
-1
3
2
Find the rate of change of CD.
−𝟏
𝑦
𝑟𝑖𝑠𝑒
Rate of change =
=
=
𝑥
𝑟𝑢𝑛
𝟐
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Neither…
The slopes of AB and CD
are not equal and are
not opposite reciprocals.
…so they are neither
parallel nor
perpendicular.
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Forms of Linear Equations
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Guided Practice
a. Write the equation to a line in slope-intercept form
perpendicular to the graph of y = -4x + 5 and
contains the point (1,-3).
Original Equation

New Equation
y = -4x + 5
m=
m = -4
Point (1, -3)
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Guided Practice
b. A line w contains the points (1, 1) and (-1, 2).
Write the equation of line p perpendicular to line w
passing through (-2, -1).
Original Equation

New Equation
(1, 1) and (-1, 2)
m=
m=?
Point (-2, -1)
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Independent practice
Directions
• Do at least 7 problems.
• If you have a question, ASK!
• Check work at the board, help your
neighbor.
• You will be turning this in for a grade.
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DOL
1) What is the slope of the line perpendicular to 2x + y = -8?
−𝟐
2) What is the slope of the line perpendicular to y – 5 =
(x + 6)?
𝟑
3) Write the equation of a line in slope-intercept form that is
𝟏
perpendicular to y = x + 6 and whose y-intercept is (0, 12).
𝟕
4) Write an equation of the line in slope-intercept form that is
perpendicular to the graph below and passes through point C.
C
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