Introduction
Lesson 6.1b – Writing Equations of Parallel and Perpendicular Lines
• ___________ lines are lines which ________ ________ or ___________.
• _________________ lines are lines which meet or intersect and create a _____
________ aka a right angle.
• We can find the equation of two lines which are parallel or perpendicular and prove whether the lines are parallel or perpendicular.
Parallel Lines
• Lines which are parallel always have the _______ ________ or value for m, but a
___________ y-intercept or value for b.
• Ex. 𝑓(𝑥) = 2𝑥 + 5 𝑎𝑛𝑑 𝑓(𝑥) = 2𝑥 − 11
are parallel lines because they have the same slope but different y-intercepts.
Ex. 1
Two lines, 𝑙
1 equation 𝑦 = 𝑎𝑛𝑑 𝑙
1
4
2
,
are linear equation. Line 𝑙
1
has the equation 𝑦 =
1
4 𝑥 + 4
. Line 𝑙
2
has the 𝑥 − 2
. Are they parallel? ___________________________________.
Ex. 2
The two lines in the graph to the right, m
1 shown. Are they parallel? and m
2
,
are 𝑚
1 𝑠𝑙𝑜𝑝𝑒:
___________________
𝑚
2
𝑠𝑙𝑜𝑝𝑒:
___________________
Are they parallel? ______________

You Try 1
You are the given two equations of two different lines, 𝑦 = 3𝑥 − 5 𝑎𝑛𝑑 𝑦 = 3𝑥 + 7.
Are these lines parallel? __________________________
You Try 2
Are these lines parallel? Explain
𝐿𝑖𝑛𝑒 1 𝑠𝑙𝑜𝑝𝑒:
___________________
𝐿𝑖𝑛𝑒 2 𝑠𝑙𝑜𝑝𝑒:
___________________
Are they parallel? ______________
Ex. 3
A line which contains the point (2,5) is parallel to the line 𝑓(𝑥) = 3𝑥 − 7
. Find the equation to this line.
1. State the point-slope formula. 2. Identify m, 𝑥
1
, 𝑎𝑛𝑑 𝑦
1
.
3. Substitute the values into the formula.
4. Simplify into slope-intercept form.

Ex. 4
Using the graph to the right, find the equation of a parallel line which passes through the point which is not on the given line.
1. Find the slope of the given line. 2. Identify m, 𝑥
1
, 𝑎𝑛𝑑 𝑦
1
.
3. Substitute the values into the point-slope formula.
4. Simplify into slope-intercept form.
You Try 3
A line which contains the point (0,-11) is parallel to the line 𝑓(𝑥) = 5𝑥 + 3
. Find the equation to this line.
1. State the point-slope formula. 2. Identify m, 𝑥
1
, 𝑎𝑛𝑑 𝑦
1
.
3. Substitute the values into the formula. 4. Simplify into slope-intercept form.

Perpendicular Lines
• Lines are always __________________ if their slopes are a ____________
___________ of one another. Perpendicular lines can have the same y-intercepts though.
• Ex. 𝑓(𝑥) = 2𝑥 + 5 𝑎𝑛𝑑 𝑓(𝑥) = −
1
2 𝑥 + 5
are perpendicular lines with the same yintercepts. Another example would be 𝑓(𝑥) = 2𝑥 + 5 𝑎𝑛𝑑 𝑓(𝑥) = −
1 𝑥 − 11
. These
2 two lines are perpendicular because of their slopes but have different yintercepts.
Ex. 5
Two lines are given,
𝑓(𝑥) = 2𝑥 − 3 𝑎𝑛𝑑 𝑓(𝑥) = −
1
2 𝑥 − 3
. Are they perpendicular?
____________________________________
Ex. 6
The two lines in the graph to the right, m
1 and m
2
, are shown. We need to determine if the two lines are perpendicular. 𝑚
1 𝑠𝑙𝑜𝑝𝑒:
___________________
𝑚
2
𝑠𝑙𝑜𝑝𝑒:
___________________
Are they perpendicular? ______________________
You Try 4
You are given two equations, 𝑦 =
11 𝑥 + 5 𝑎𝑛𝑑 𝑦 = −
5
5
11 𝑥.
Are these two lines perpendicular?
____________________

You Try 5
The two lines in the graph to the right, line 1 and line 2
,
are shown. We need to determine if the two lines are perpendicular.
𝐿𝑖𝑛𝑒 1 𝑠𝑙𝑜𝑝𝑒:
___________________
𝐿𝑖𝑛𝑒 2 𝑠𝑙𝑜𝑝𝑒:
___________________
Are they perpendicular? _____________
Ex. 7
A line which contains the point (2,5) is perpendicular to the line 𝑓(𝑥) = 3𝑥 − 7
. Find the equation to this line.
1. State the point-slope formula. 2. Identify m, 𝑥
1 reciprocal of m.
, 𝑎𝑛𝑑 𝑦
1
.
Find the negative
3. Substitute the values into the formula. Use the new slope you found for m.
4. Simplify into slope-intercept form.

Ex. 8
Using the graph to the right, find the equation of a perpendicular line which passes through the point which is not on the given line.
1. Find the slope of the given line. 2. Identify m, 𝑥
1 reciprocal of m.
, 𝑎𝑛𝑑 𝑦
1
.
Find the negative
3. Substitute the values into the point-slope formula. Use the new slope you found form.
4. Simplify into slope-intercept form.
You Try 6
• A line which contains the point (0,5) is perpendicular to the line 𝑓(𝑥) = −
2
5 𝑥 − 5
. Find the equation to this line.
1. State the point-slope formula. 2. Identify m, 𝑥
1 reciprocal of m.
, 𝑎𝑛𝑑 𝑦
1
.
Find the negative
3. Substitute the values into the formula. Use the new slope you found for m.
4. Simplify into slope-intercept form.