Name: ________________ Per.: _____ Date: ____
Linear Equations – Day 8: Graphing Parallel &Perpendicular Lines
DO NOW:
Graph the following equations on the grid to the right.
1)
y =
2
x + 2
3
1
2
3) y = - x - 1
2) y + 3 =
4)
2
x
3
y = 2x - 1
a) What kind of lines are #1 & 2 ? __________________________________
b) What do you notice about the equations for lines #1 & 2? _______________
______________________________________________________________________________________
c) What kind of lines are #3 & 4 ? __________________________________
d) What do you notice about the equations for lines #3 & 4? _______________
_______________________________________________________________________________________
OBJECTIVE: By the end of this lesson, I will be able to ________________
______________________________________________________________
DEMO:
1) Looking at two equations, we can tell the lines are parallel if _______________
2) Looking at two equations, we can tell the lines are perpendicular if __________
3) What is the reciprocal of 2? _____ 4) What is the negative reciprocal of 2? _____
3
5
3
5
5) What is the reciprocal of - ? ____ 6) What is the negative reciprocal of - ? ____
7) What do you notice about the product of the slopes of the perpendicular lines?
______________________________________________________________
Examples:
Let’s Try it!!!!!!!!!!!
1) Graph the equation:
y =
3
x + 2
4
a) What is the slope of the line parallel to
the given equation? ____________
Given -1 as the y-intercept, graph this line.
b) What is the equation of this line?
____________________________________
c) What is the slope of the line perpendicular
to the given equation? ________
Given 2 as the y-intercept, graph this line.
d) What is the equation of this line?
e) Why is the line you graphed in part c) perpendicular to the line graphed in
part a) ? Explain. ______________________________________________
____________________________________________________________
CLASSWORK
Find the slope of a line parallel to the following equations.
1) y =
1
x + 3
2
4) y = 0
2
3
2) y = - x – 1
3) -3(2x -1) = y
5) 2x – y = 0
*6) 15x – 12y = 7
Find the slope of a line perpendicular to the following equations.
7) y =
4
x + 1
5
10) y = -2x + 1
8) 5y = 7x – 2
9) y – 5 =
11) y = 2x
9
x
2
12) y = -x
Tell whether the lines for the pair of equations are parallel or perpendicular.
1
4
13) y = - x + 4
y = 4x + 6
________________
14) y =
y =
x
- 4
3
1
x + 2
3
_________________
15) y = x
y = -x + 4
_______________
Tell whether the lines for the pair of equations are parallel or perpendicular.
1
3
16) y + 5 = - x
Y – 3x = 2
________________
1
3
17) y = 1 x + 3
y - 2 =
4
x
3
_________________
18) 2y = 3x - 2
2y = y -
2
x + 4
3
_______________
HOMEWORK
Find the slope of a line parallel to the following equations.
1) y =
7
x + 6
8
4) y = 1
4
5
2) y = - x – 3
5) 2y = 5x + 2
3) -2(4x + 3) = y
*6) 15x – 12y = 7
Find the slope of a line perpendicular to the following equations.
7) y =
6
x – 3
7
10) y = -4x + 1
8) 3y = 4x – 6
11) y = -3x
9) y + 6 =
7
x
2
12) y = x
Tell whether the lines for the pair of equations are parallel or perpendicular.
Explain why? Graph the equations
13) y -
y =
x
= - 3
2
1
x + 4
2
________________
14) y – 2x = 0
1
5
15) y = - x – 3
y = -2x + 5
y = 5x + 9
_________________
_______________
1. Which equation represents a line parallel to the line y = 2x – 5?
(1) y = 2x + 5
(2) y = – x – 5
(3) y = 5x – 2
(4) y = –2x – 5
2. Which equation represents a line that is parallel to the line whose equation is
2 x  3y  12
(1) 6 y  4 x  2
( 2) 6 y  4 x  2
?
(3) 4 x  6 y  2
(4) 6 x  4 y  2
3. Which equation represents a line that is perpendicular to the line whose equation is
2 y  3x  7 ?
(1) y  x  7
( 2) 2 y  3x  3
4.
2
x3
3
3
(4) y  x  3
2
(3) y 
Which line is perpendicular to the line whose equation is 5 y  6  3 x ?
5
(l) y   x  7
3
5
(2) y  x  7
3
3
(3) y   x  7
5
3
(4) y  x  7
5
5. Which statement describes the lines whose equations are y 
(1) They are segments.
(2) They are perpendicular to each other.
(3) They intersect each other.
(4) They are parallel to each other.
1
x  12 and 6 y  2 x  6 ?
3
6.
Which properties best describe the coordinate graph of two distinct parallel lines?
(1) same slopes and same intercepts
(2) same slopes and different intercepts
(3) different slopes and same intercepts
(4) different slopes and different intercepts
7. If two lines are parallel and the slope of one of the lines is m, what is the product of
their slopes?
(1) 1
(2) 2m
(3) m 2
(4) 0
8. If the product of x and
(1) m
(2) m
1
is 1, m  0, then x is equivalent to
m
(3) 1 m
1
(4) 
m