Transcript Chapter_3.3_Slopes_of_Lines_web

Chapter 3.3 Slopes of Lines
Check.3.1 Prove two lines are parallel, perpendicular, or
oblique using coordinate geometry.
Spi.3.1 Use algebra and coordinate geometry to
analyze and solve problems about geometric figures
(including circles).
Objective: Be able to calculate slope of line
and determine if lines are parallel,
perpendicular or neither
Slope
m = rise
run
= change in y.
change in x
= y2 – y1
x 2 – x1
Horizontal Line, m= 0
Vertical Line, m = undefined
Lines are parallel if m = m
Lines are perpendicular if m = -1/m
What is the slope?
4 –4
m=
2
m= 0
-3 –4
m=
3-3
-7
m=
0
m = undefined
Slope of Parallel and
Perpendicular Lines
Two non-vertical lines have the same slope if and only if
they are parallel
Two non-vertical lines are perpendicular if and only if the
product of their slopes is -1
y = 3/4x + 2
m = 3/4
y = 3/4x - 5 is ________
Parallel
Perpendicular
y = -4/3x + 3 is ____________
Parallel and
Perpendicular Lines
• y = 2x + 2
• Parallel Line through (0,0)
• y = 2x
• Perpendicular through (0,0)
• y=-½x
Determine line relationships
• Determine whether AB and CD are parallel, perpendicular
or neither
• A (-2, -5) B(4, 7) C(0, 2) D(8, -2)
7–(-5)
AB=
4 –(-2)
12
AB=
6
AB=2
-2 –2
CD=
8 –0
-4
CD=
8
CD= - 1/2
Perpendicular
Determine line relationships
• Determine whether AB and CD are parallel, perpendicular
or neither
• A (-8, -7) B(4, -4) C(-2, -5) D(1, 7)
-4–(-7)
AB=
4 –(-8)
3
AB=
12
AB=1/4
7-(-5)
CD=
1-(-2)
12
CD=
3
CD= 4
Neither
Use Slope to find a line
• Draw a line containing P (-2,1) and is perpendicular to JK
with J(-5, -4) and K(0,-2)
•
-2–(-4)
Perpendicular Slope = -5/2
JK=
0 –(-5)
2
JK=
5
y = -5/2x - 4
Write equation from 2 points
• A (-1, 6) and B (3, 2)
2 –6
m=
3 –(-1)
-4
m=
4
m= -1
y = mx + b
6 = -1(-1) + b
6=1+b
5= b
y = -x + 5
Write equation from 2 points
• A (4, 9) and B (-2, 0)
0 –9
m=
-2 –4
-9
m=
-6
m= 3/2
y = mx + b
9 = 3/2(4) + b
9=6+b
3= b
y = 3/2x + 3
Practice Assignment
• Block - Page 190, 12 - 36 every 4th