4.3 Parallel and Perpendicular Lines

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4.3 Parallel and Perpendicular Lines
4.3 Parallel and
Perpendicular Lines
Algebra 2/Geometry
High School
Teacher Page
Content: Write the equation of a parallel or
perpendicular line to a given line, in slope
intercept form.
 Grade Level: Algebra 2/Geometry
 Creator: Don Sutcliffe
 Other – Print slides 13-20 as a handout for
students to take notes.

MAP TAP 2003-2004
Parallel and Perpendicular Lines
2
Teacher Page

Curriculum Objectives:


Algebra 2 – II.A – The learner will find the slope
of a linear equation and the relationships of the
slopes of parallel and perpendicular lines.
MAP Objectives:
Missouri Show-Me Standard – Math – MA1,
MA2, MA4, MA5
 Missouri Show-Me Standard – Goal – G1.6,
G3.4, G3.5, G4.1

MAP TAP 2003-2004
Parallel and Perpendicular Lines
3
Parallel Lines

Two non-vertical lines are parallel if
and only if their slopes are equal.


If l1║l2, then m1= m2.
If m1= m2, then l1║l2.
m1
l1
MAP TAP 2003-2004
Parallel and Perpendicular Lines
m2
l2
4
Write the equation of the line that passes
through (3,6) and is parallel to y = 2/3x+2.
m = 2/3 and the point is (3,6)
y = mx+b
6 = 2/3(3)+b
6 = 2+b
4=b
y = 2/3x+4
MAP TAP 2003-2004
Parallel and Perpendicular Lines
5
Write the equation of the line that passes
through (4,-5) and is parallel to y = -2x-4.
m = -2 and the point is (4,-5)
y = mx+b
-5 = -2(4)+b
-5 = -8+b
3=b
y = -2x+3
MAP TAP 2003-2004
Parallel and Perpendicular Lines
6
Write the equation of the line that passes
through (-6,4) and is parallel to y=1/3x-1.
m=1/3 and the point is (-6,4)
y =1/3x+6
MAP TAP 2003-2004
Parallel and Perpendicular Lines
7
Perpendicular Lines

Two non-vertical lines are
perpendicular if and only if the
product of their slopes is -1.


If l1┴l2, then m1 ● m2= -1.
l1
If m1● m2 = -1, then l1┴l2.
Slopes are negative
reciprocals
MAP TAP 2003-2004
Parallel and Perpendicular Lines
m1
m2
l2
8
Write the equation of the line that passes through
(6,-5) and is perpendicular to y = 2x+3.
m = -1/2 and the point is (6,-5)
y = mx+b
-5 = -1/2(6)+b
-5 = -3+b
-2 = b
y = -1/2x-2
MAP TAP 2003-2004
Parallel and Perpendicular Lines
9
Write the equation of the line that passes through
(6,-7) and is perpendicular to y = 2/3x+1.
m = -3/2 and the point is (6,-7)
y = mx+b
-7 = -3/2(6)+b
-7 = -9+b
2=b
y = -3/2x+2
MAP TAP 2003-2004
Parallel and Perpendicular Lines
10
Write the equation of the line that passes through
(-4,-3) and is perpendicular to y = x+6.
m = -1 and the point is (-4,-3)
y = -x-7
MAP TAP 2003-2004
Parallel and Perpendicular Lines
11
End Show
MAP TAP 2003-2004
Parallel and Perpendicular Lines
12
Parallel Lines

Two non-vertical lines are parallel if
and only if their slopes are equal.


If l1║l2, then m1= m2.
If m1= m2, then l1║l2.
m1
l1
MAP TAP 2003-2004
Parallel and Perpendicular Lines
m2
l2
13
Write the equation of the line that passes
through (3,6) and is parallel to y = 2/3x+2.
m = _____ and the point is (__,__)
y = mx+b
MAP TAP 2003-2004
Parallel and Perpendicular Lines
14
Write the equation of the line that passes
through (4,-5) and is parallel to y = -2x-4.
m = ____ and the point is (__,__)
MAP TAP 2003-2004
Parallel and Perpendicular Lines
15
Write the equation of the line that passes
through (-6,4) and is parallel to y=1/3x-1.
m=___ and the point is (__,__)
MAP TAP 2003-2004
Parallel and Perpendicular Lines
16
Perpendicular Lines

Two non-vertical lines are
perpendicular if and only if the
product of their slopes is -1.


If l1┴l2, then m1 ● m2= -1.
l1
If m1● m2 = -1, then l1┴l2.
m1
m2
l2
MAP TAP 2003-2004
Parallel and Perpendicular Lines
17
Write the equation of the line that passes through
(6,-5) and is perpendicular to y = 2x+3.
m = ___ and the point is (__,-__)
MAP TAP 2003-2004
Parallel and Perpendicular Lines
18
Write the equation of the line that passes through
(6,-7) and is perpendicular to y = 2/3x+1.
m = ____ and the point is (__, __)
MAP TAP 2003-2004
Parallel and Perpendicular Lines
19
Write the equation of the line that passes through
(-4,-3) and is perpendicular to y = x+6.
m = ___ and the point is (__,__)
MAP TAP 2003-2004
Parallel and Perpendicular Lines
20

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