G-GPE.5: Prove the slope criteria for parallel and perpendicular lines. Guided Notes: Parallel and Perpendicular Lines Name_________________________
Using what we learned yesterday: Put the equation in slope-intercept form 1. 2. Parallel Lines: Graph each of the following lines on the same graph. Examine the equation of the lines to determine relationships between the two lines. Equation of Line 1: ___________________ Equation of Line 2:____________________
What is the relationship between lines that are ____________________? ___________________________________________________________
___________________________________________________________
___________________________________________________________
Perpendicular Lines: Graph each of the following lines on the same graph. Examine the equation of the lines to determine relationships between the two lines. Equation of Line 1: ___________________ Equation of Line 2:____________________
What is the relationship between lines that are __________________? _________________________________________________________
_________________________________________________________
_________________________________________________________
Y X 3 y TY
y Zyx 3 y EfxtY
The lines are
Neither
4 2 1 4 12
1
e
The Lines are perpendicularo
d thele
G-GPE.5: Prove the slope criteria for parallel and perpendicular lines. Summarize:
x Parallel lines have the _______________ slope.
x Perpendicular lines have _________________ (sign change) AND _____________________ (“flip it”) slopes of each other.
o Note: If two lines are ________________________, then the product of their slope is __________.
Practice:
Original Slope Parallel Slope Perpendicular Slope
Are the following lines parallel, perpendicular or neither???
x
x
x
Writing the equation of a line that is parallel or perpendicular to another equation.
1. Get the line given in ____________________________________ form.
2. Take the correct _____________ from the line given 3. Write the equation of the new line using the ____________________________ and the ________________ you
found.
𝑚 0
𝑚
𝑚 𝑏𝑎
𝑚
𝑚
𝑚
𝑚 𝑎𝑏
𝑚 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
Slope Bank
Sameopposite reciprocal
Iperpendicular2Hz
m E m b Ib am Z m Igm m 2
Zm o m f undefined
2Slope
_Undef
r
in iinNeither 4 34 3 8 21 64 46 4 3 8 V
Slope Intercept y mxtb
y mXtb
point Slope slope Intercept
Y Y _mex x 9
G-GPE.5: Prove the slope criteria for parallel and perpendicular lines.
Practice Together: 1. Write the equation of a line in slope-intercept form that passes through the point (-6, -9) and is parallel to
2. Write the equation of a line in standard form that passes through the point (7, 1) and is perpendicular to 3
Individual Practice: 1. Write the equation of a line that passes through (-2, 3) and is parallel to
2. Write the equation of a line that passes through (4, -10) and is perpendicular to 0 Connection to Geometry:
x Plot the points below and join the points from A to D in order. A(-1, -3) B(0, -4) C(2, -2) D(1, -1)
x What is the slope of AD? ___________ of BC?_______________
x What is the slope of AB?____________ of DC?______________
x What is the slope of AB?____________ of BC?_______________
x What is the slope of AD?________ ___of DC?_______________
x What can you say about AD and DC?_________________________________________________________
x What can you say about AB and BC?_________________________________________________________
x What is this figure called?__________________________________________________________________
Tea z
e
y zxtfp.int a4Yyf9Ez2ffIg ay 2X G
p D
siE I fxpoint 7 a A yB 3C 25
a l
l I D
l I tfcB
l 1
AD is perpendicular to Dc
AB is parallel to BC
Regtangle
G-GPE.5: Prove the slope criteria for parallel and perpendicular lines.
Parallel vs. Perpendicular Practice Name____________________
Compared to
PARALLEL PERPENDICULAR NEITHER
Organize the equations to
left in the table above!!!
PerpendicularHopeis
4 4 8 3 7 12 11 103
154 511 12 3X y y 511 8
X 34 36 Y 1311 18 4 46 X
y rtgXt9 y 3 8 8 24 10
UX 124 6 6 124 24 4 4 92 167 10 4 1 174 3 12 127 38 4
y tgx
3 12 74 5 8
Y a3X
4 13 12 4 4 5
4 3 13
4 4 12 4 13 108
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