Parallel and Perpendicular
lines
I can write an equation of a line that
passes through a given point, either
parallel or perpendicular to a given
line.
What are parallel lines?
Lines in the same plane that
do not intersect are called
parallel lines.
What do you think is
true about the slopes of
parallel lines?
The slopes are equal.
What is the slope of a line
parallel to the given line?
What is the slope of
the given line?
m=2
What is the slope of a
line parallel to the
given line? m = 2
2 forms to write linear equations.
1. Slope-intercept form.
m = slope
y = mx + b
b= y-intercept
2. Point-slope form.
y  m( x  x1)  y
1
y2 - y1
vertical
change
(rise)
change
in
y
slope =

 x -x
horizontal change (run) change in x
2
1
Write an equation in slope-intercept form for
the line that passes through (-3, 5) and is
parallel to the graph of y = 2x – 4.
Slope =___
2 in the given line.
Slope = ___
2 in the new line parallel to y = 2x – 4.
y = m(x – x1) + y1
y = 2 (x – -3 ) + 5
y = 2 (x + 3) + 5
y = 2x + 6 + 5
y = 2x + 11
Write an equation in slope-intercept form for
the line that passes through (1, 3) and is
parallel to the graph of -4x + y = – 5.
Slope = ___
4
in the given line.
y =4x - 5
Slope = ____
4
in the new line parallel to -4x + y = -5
y = m(x – x1) + y1
y = 4 (x – 1 ) + 3
y = 4x - 4 + 3
y = 4x - 1
What are Perpendicular lines?
Lines that intersect at right
angles are called
perpendicular lines.
What do you think is
true about the slopes of
perpendicular lines?
The slopes of perpendicular
lines are opposite reciprocals
of each other.
The slopes of perpendicular lines are opposite
reciprocals of each other.
Examples of Reciprocals:
2
,
3
3
2
4
,
5
5
4
2,
1
2
Examples of Opposite reciprocals
4 3
,
3
4
3 5
,
5
3
 6, 1
6
What is the slope of a line
perpendicular to the given line?
What is the slope of
the given line?
m=2
What is the slope of a
line perpendicular to
the given line?m = - ½
Write an equation in slope-intercept form for the line
that passes through (2, 3) and is perpendicular to the
graph of y = ⅓ x – 5.
Slope = ___
⅓ in the given line.
Slope = ____
-3 in the new line perpendicular to y = ⅓ x - 5.
y = m(x – x1) + y1
y = -3 (x – 2 ) +3
y = -3x + 6 + 3
y = -3x + 9
Write an equation in slope-intercept form for the line
that passes through (-6, 4) and is perpendicular to the
graph of 2x + y = 5
Slope = _____
-2 in the given line.
y = -2x + 5
Slope = ___
½ in the new line perpendicular to 2x + y = 5
y = m(x – x1) + y1
y = ½ (x – -6 ) + 4
y=
½ (x + 6 ) + 4
y =½ x + 3 + 4
y=½x+7
homework
WS: pg 334: 7-15, 19-22, 28-30,
38-46 evens