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