Download Parallel and Perpendicular Lines

Name _______________________________________ Date ________________ Period______
Notes: Parallel and Perpendicular Lines
Parallel Lines
Perpendicular Lines
SAME SLOPE but Different
y-intercept
y = 2x+1
m=2
Slopes are OPPOSITE
RECIPROCALS
y = 2x+1
y = 3 - ½x
m=2
m=-½
y = 3+2x
m=2
Horizontal Lines are parallel
y = -2
y=8
m=0
m=0
Vertical and Horizontal Lines are
perpendicular to each other
y = -4
x=1
m = 0 m = undefined
Vertical Lines are parallel
x=3
x = -4
m = undefined m = undefined
Identifying Parallel and Perpendicular Lines
Ex1: Given the slope m = -2 , find the following:
a) the slope of a parallel line
m = ______
b) the slope of a perpendicular line
m = ______
c) the slope of a line neither parallel or perpendicular
m = ______
Your Turn
Ex2: Given the slope m = 3/4 , find the following:
a) the slope of a parallel line
m = ______
b) the slope of a perpendicular line
m = ______
c) the slope of a line neither parallel or perpendicular
m = ______
Ex 3: What is the slope of…
a) a line parallel to the line y = 3x + 2
m=
b) a line perpendicular to the line y = -11 – 5x
m=
c) line perpendicular to the line x = 8
m=
d) a line parallel to the line y = -x + 5
m=
e) a line perpendicular to the line 3x - 2y = 4
m=
Name: ______________________________________________
Date: _______________
Are the following lines parallel?
1. y  4x  2
y  9  4x
2. y  7
y  2
Are the following lines perpendicular?
5. y  5x  2
6. y  2x
1
1
y x4
y  x4
5
2
3. y 
1
x 6
2
2
x2
3
2x  3y  6
4. y 
2x  4y  3
7. y  x
y  x
9. y  4x  2
x  4y  8
8. y  3
x  3
In each box you will write in “Parallel to _________” or “Perpendicular to _________”
y
4
x 1
5
x  3
1
y x4
2
1
y  2 x
3
y5
y  3x  4
2
y x
3
5
y  2 x
4
y  4x
y  3x  1
y  3 x
y
3
x  10
2
Identify which lines are parallel.
Identify which lines are perpendicular.
1. Line1: 2x  5y  10
2
Line2 : y 
5
Line3 : 4x  10y  20
2
Line4 : y  x  1
5
2. Line1: y 
6
x
7
7
Line2 : y  x  2
6
Line3 : 7x  6y  14
6
Line4 : y   x  2
7
Writing Equations Parallel and Perpendicular Lines
Ex 1: Write the equation of the line with a y-intercept of 4 and perpendicular to y = 2x + 1.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using
y = mx + b or y – y1 = m(x – x1).
Ex 2: Write the equation of the line with a y-intercept of -2 and parallel to y = 4/5x.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using
y = mx + b or y – y1 = m(x – x1).
Ex 3: Write an equation in slope-intercept form for the line that passes through (4, 10) and is
parallel to the line described by y = 3x + 8.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using
y = mx + b or y – y1 = m(x – x1).
Ex 4: Write an equation in slope-intercept form for the line that passes through (2, –1) and is
perpendicular to the line described by y = 2x – 5.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using
y = mx + b or y – y1 = m(x – x1).
Ex 5: Write an equation in slope-intercept form for the line that passes through (5, 7) and is
4
parallel to the line described by y = x - 6 .
5
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using
y = mx + b or y – y1 = m(x – x1).
Ex 6: Write an equation in slope-intercept form for the line that passes through (–5, 3) and is
perpendicular to the line described by y = 5x.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using
y = mx + b or y – y1 = m(x – x1).
Ex 7: Write an equation in slope-intercept form
that is perpendicular to the graph and has a y-intercept of -3.
Ex 8: The graph of a linear function f(x) is parallel to the line described by y = -½x – 1 and
contains the point (-4, -1). What is the y-intercept of the linear function f(x)?