Download GRAPHING LINEAR EQUATIONS

GRAPHING LINEAR
EQUATIONS
PARALLEL
VS
PERPENDICULAR
LINES
WARM-UP:
Find the slope and y-intercept of the following linear
equations
1. Y + 3 = 2x 2. Y + 3x = -6
Y = 2x - 3
Slope: 2
Y-int: -3
Y = -3x - 6
Slope: -3
Y-int: -6
3. y - x - 21= 3
Y = x + 24
Slope: 1
Y-int: 24
4. 3Y + 9 = 6x 5. 2y + 3 = 2x 6. 4y - x - 2= 3
Y = 2x - 3
Y = x - 3/2
Y = x/4 +5/4
Slope: 2
Slope: 1
Slope: 1/4
Y-int: -3
Y-int: -3/2
Y-int: 5/4
Parallel lines
Parallel lines are linear equations which have the
same slope
Examples:
Y=2x+9
Y=2x-23
Y=1/3x +10
Y=1/3x +5
Y=x +10
Y=7 +x
Counter-examples:
Y=-2x+9
Y=2x-23
Y=1/3x +10
Y=3x +5
Y=5x +10
Y=7 +x
Example:
2x + 6y = 12
-2x
-2x
6y = -2x + 12
6
6
6
y = -2/6 x + 2
y = -1/3 x + 2
Is parallel to
y = -1/3 x + 5
REVIEW
Find the reciprocal of the following numbers:
1.
⅔
3/2
2.
⅜
3.
8/3
7
4.
1/7
1/9
9
Find the negative reciprocal of the following numbers:
1. ½
-2
2. 4/9
-9/4
3.
8/7
-7/8
4.
3
-⅓
Perpendicular lines
THE LINES ARE
PERPENDICULAR IF THE
PRODUCT OF THEIR SLOPES
Examples:
IS -1.
Y=2x+9
Y=-½x-23
Y=1/3x +10
Y=-3x +5
Y=x +10
Y=-1X +21
Counter-examples:
Y=-2x+9
Y=-2x-23
Y=⅓x +10
Y=3x +10
Y=5x +10
Y=7 +x
Example:
Write an equation that is
perpendicular to the
following:
1. Y = 2/3x + 7
Y = -3/2x + 7
3. Y = -1/9x + 29
Y = 9x + 879
2. Y = 7x -9
Y = -1/7x + 25
4. Y = -5x - 6
Y = -⅕x + 25
Practice
re the equations parallel to each other?
no
no
yes
yes
yes
yes
Which one is a parallel line? Which one is a
perpendicular line?
perpendicular
perpendicular
parallel
niether