Equations of Parallel and
Perpendicular Lines
ALGEBRA 1 UNIT 5: WRITING EQUATIONS OF LINES
Parallel Lines
What are parallel lines?
 Parallel
lines are two lines that never
intersect each other.
Where have you seen
examples in real-life?
 Lines
on a road
 Lines between bricks
 Floor and ceiling
Brainstorm
as many examples of
parallel lines as possible.
What characteristics do
parallel lines have?
 Parallel
lines are two lines that never
intersect each other, BUT:

What are their features on a graph?
They
have the same slope
They
can have different y- intercepts
They
still will never intersect
Parallel Lines
Determine if lines are
parallel or perpendicular
 1.
Put the equation into slopeintercept form ( y = mx +b)
 2. Determine if the slopes are the
same (parallel) or opposite
reciprocals (perpendicular) or
neither.
Determine if the lines are
parallel
Y
= 4x + 16
 Y = 3x + 1
 Y = -4x – 1
 Y = -1/4x – 4
 Y = 4x - 2
Determine if two lines are
parallel
 2x
+ 4y = 10
 9x + 4y = 12
 Y = -9/4x – 5
 2y = 18/4x + 8
 Y = - 3x – 1
Writing equations of parallel
lines
I
want a line parallel to
y = 4x + 10 that goes
through the point (6, 12).
How
would I do this
graphically?
Writing equations of parallel
lines
I
want a line parallel to
y = 4x + 10 that goes
through the point (6, 12).
How
would I do this
algebraically?
Example
I
want a line parallel to y = -2x – 1
and through the point (3, 6).
Example
I
want a line parallel to y = 6x + 12
and through the point (0, -10).
Real- Life Example
I
am creating a city which is to have
two parallel streets. If I plot the first
street such that the equation is
y = 2x – 2 and I want the other street
to be 6 units away, what would be
the equation of this street?
Real-Life Example
Questions?
Perpendicular
Lines
What are perpendicular
lines?
 Perpendicular
lines are two lines that
intersect to form a right angle.
 A right angle is an angle whose
measure is 90 degrees.
Where have you seen
examples in real-life?
 Floor
and wall
 Intersection of two roads
 Tiles on the ground
Brainstorm
as many examples of
parallel lines as possible.
What characteristics do
perpendicular lines have?
 Perpendicular
lines are two lines that
intersect to form a right angle, BUT:

What are their features on a graph?
They
have opposite reciprocal slopes
WHY?
They
can have different y- intercepts
Perpendicular Lines
Determine if two lines are
perpendicular
x
- 3y = 10
 9x + 4y = 12
 Y = -9/4x – 5
 2y = 18/4x + 8
 Y = - 3x – 1
Write equations of
perpendicular lines.
I
want a line perpendicular
to y = 4x + 10 that goes
through the point (6, 12).
How
would I do this
graphically?
Write equations of
perpendicular lines.
I
want a line perpendicular
to y = 4x + 10 that goes
through the point (6, 12).
How
would I do this
algebraically?
Example
I
want a line perpendicular to
y = -2x – 1 and through the point
(3, 6).
Example
I
want a line parallel to y = 6x + 12
and through the point (0, -10).
Real- Life Example
I
am designing an intersection. I need the
two streets to create a 90 degree angle. If
the first street is located on the line y = 4x –
2 where would I need to build the new
road to create this intersection such that
the road goes through a town located at a
point (4, 7)?
Real- Life Example