### 5.5 parallel and perpendicular

```Lesson 5.5
Parallel and Perpendicular
Lines
Alg 7.0
Derive linear equations by using the
point-slope formula.
Alg 8.0
Understand the concepts of parallel
lines and perpendicular lines and how
those slopes are related. Find the
equation of a line perpendicular to a
given line that passes through a given
point.
Lesson Objective:
Students will be able to write
equations of parallel and
perpendicular lines as
demonstrated by a Ticket out
the Door.
Graph the following on the coordinate plane.
y
1
1
y  x3
y  x 1
2
2
1
m
2
b  3
x
1
m
2
b  1
Parallel lines have the same slope.
Parallel lines
Two lines are parallel if they never intersect.
Example:
Parallel lines
Not parallel lines
Think Pair What do we know
parallel lines?
Graph the following on the coordinate plane.
2
3
y  x 1
y   x4
y
3
2
2
3
m
m
3
2
b 1
x
b4
Lines appear
perpendicular
Perpendicular lines have slopes that are
opposite reciprocals
Perpendicular Lines
Two lines are perpendicular if they intersect to form right angles.
Example:
Perpendicular
Not perpendicular
Think Pair What do we know about the
of perpendicular lines?
Share: Linesslope
are perpendicular if the product of the
slopes is -1
(opposite and reciprocal).
I Do!
Find the slope only of a line parallel and
perpendicular to the graph of each
equation.
Example 2:
Example 1:
m=2
2
y   x 1
3

We Do!
Find the slope of a line parallel and
perpendicular to the graph of each
equation.
y  3  4( x  2)
We Do!
Find the slope of a line parallel and
perpendicular to the graph of each
equation.
Think Pair Share:

3x  4 y  12
You Do!
Find the slope of a line parallel and
perpendicular to the graph of each
equation.
Partner A on the  2 x  y  2
White Board
Partner B on the
White Board

7x  y  5
Determine if the lines in each pair are
parallel or perpendicular?
3
y  x2
2
3x  2 y  8
Part 1: Parallel Lines
Parallel lines:
Lines are parallel if they have the
same slope but different y-intercepts.
Write in slopeintercept form
the equation of
the line that is
parallel to the
line in the graph
and passes
through
the given point.

Flow map for parallel lines:
Step 1:
Determine
the slope
that you
will need
m=
Step 2:
take the
given
point
x1 =
y1 =
Step 3: plug
the point
and slope
into the
point - slope
formula
Step 4:
distribute
and solve
for “y”
y = mx + b
y – y1 = m(x – x1)
Point-Slope
Form
Stop here if the question asks for Point Slope Form
SlopeIntercept
Form
I Do!
Write in slope-intercept form the
equation of the line that is parallel
to the line y  3x  5 and passes
through the point (6, 2).
We Do!
Write in slope-intercept form the
equation of the line that is parallel
to the line y  2 x  6
and
passes through the point (-4, -6).
You Do!
Partner A on the Whiteboard:
Write in slope-intercept form the
equation of the line that is parallel to the
line y  6 x  2 and passes through
the point (0,1).
You Do!
Partner B on the Whiteboard:
Write in slope-intercept form the
equation of the line that is parallel to the
line y  2 x  3 and passes through
the point (-3,5).
Part 2: Perpendicular Lines
Perpendicular lines
Lines are perpendicular if the product
of their slopes equals −1
The slopes are:
*opposite
*reciprocal
Write in slopeintercept form the
equation of the line
that is
perpendicular to the
line in the graph
and passes through
the given point.

I Do!
Write in slope-intercept form the
equation of the line that is
perpendicular to the line y  3x  5
and passes through the point (6, 2).
We Do!
Write in slope-intercept form the
equation of the line that is
perpendicular to the line y  2 x  7
and passes through the point (0, 1).
You Do! Partner A on the Whiteboard
Write in slope-intercept form the
equation of the line that is
perpendicular to the line y  x  3
and passes through the point (-1, 2).
You Do! Partner B on the Whiteboard
Write in slope-intercept form the
equation of the line that is
1
perpendicular to the line y   4 x  2
and passes through the point (-1, -2).
Summary
• Parallel Lines: They have the same exact slope (m)
and different y-intercepts (b)
• Perpendicular Lines: Their slopes are opposite
(change the sign) and reciprocals (flip)of each
other.
```