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 __________________?

_________________________________________________________

_________________________________________________________

_________________________________________________________

G-GPE.5: Prove the slope criteria for parallel and perpendicular lines. Summarize:

Parallel lines have the _______________ slope.

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???

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 𝑏

𝑎

𝑚

𝑚

𝑚

𝑚 𝑎

𝑏

𝑚 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑

Slope Bank

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:

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)

What is the slope of AD? ___________ of BC?_______________

What is the slope of AB?____________ of DC?______________

What is the slope of AB?____________ of BC?_______________

What is the slope of AD?________ ___of DC?_______________

What can you say about AD and DC?_________________________________________________________

What can you say about AB and BC?_________________________________________________________

What is this figure called?__________________________________________________________________

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!!!