5-8 slopes of parallel and perpendicular lines -...
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5-8 Slopes of Parallel and Perpendicular Lines
Warm Up Find the reciprocal.
1. 2 2.
3.
Find the slope of the line that passes through each pair of points. 4. (2, 2) and (–1, 3)
5. (3, 4) and (4, 6)
6. (5, 1) and (0, 0)
5-8 Slopes of Parallel and Perpendicular Lines
1. The student is able to identify if lines are parallel or perpendicular
5. The student is able to write equations of parallel and perpendicular lines
Learning Goals
5-8 Slopes of Parallel and Perpendicular Lines
To sell at a particular farmers’ market for a year, there is a $100 membership fee. Then you pay $3 for each hour that you sell at the market. However, if you were a member the previous year, the membership fee is reduced to $50.
• The red line shows the total cost if you are a new member.
• The blue line shows the total cost if you are a returning member.
5-8 Slopes of Parallel and Perpendicular Lines
Parallel lines are lines in the same plane that have no points in common. In other words, they do not intersect.
Perpendicular lines are lines that intersect to form right angles (90°).
5-8 Slopes of Parallel and Perpendicular Lines
5-8 Slopes of Parallel and Perpendicular Lines
5-8 Slopes of Parallel and Perpendicular Lines
Helpful Hint
If you know the slope of a line, the slope of a perpendicular line will be the "opposite reciprocal.”
5-8 Slopes of Parallel and Perpendicular Lines
Example 1: Identifying Parallel Lines Identify which lines are parallel or perpendicular.
1. y = 53x − 2
2. y = x
3. y = 53x + 4
4. y = x +1
A. m=___
m=___
m=___
m=___
5-8 Slopes of Parallel and Perpendicular Lines
1. y = 2x −3
2. y = − 23x +3
3. 2x +3y = 8
4. y+1= 3 x −3( )
Identify which lines are parallel or perpendicular.
B.
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
1. y = 2x −3
2. y = − 23x +3
3. 2x +3y = 8
4. y+1= 3 x −3( )
Identify which lines are parallel or perpendicular.
B. m=___
m=___
m=___
m=___
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
1. y = 2x −3
2. y = − 23x +3
3. y = − 23+
83
4. y = 3x −10
Identify which lines are parallel or perpendicular.
B. m=___
m=___
m=___
m=___
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are parallel or perpendicular.
1. x = −2
2. y =1
3. y = −4x
4. y+ 2 = 14x + 4( )
C. m=___
m=___
m=___
m=___
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
1. y = 2x + 2
2. y = 2x + 1
3. y = –4
4. x = 1
Identify which lines are parallel or perpendicular. a. m=___
m=___
m=___
m=___
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are parallel or perpendicular.
1. y = 34x +8
2. −3x + 4y = 32
3. y = 3x
4. y−1= 3 x + 2( )
b. m=___
m=___
m=___
m=___
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are parallel or perpendicular.
1. y = 43x +3
2. y = 2
3. y = 43x − 5
4. y = −3
c. m=___
m=___
m=___
m=___
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are parallel or perpendicular. 1. y = 3x + 2
2. y = − 12x + 4
3. x + 2y = −4
4. y− 5= 3 x −1( )
d. m=___
m=___
m=___
m=___
Example 1: Identifying Parallel Lines
5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are parallel or perpendicular.
1. y = 3
2. x = −2
3. y = 3x
4. y = 13x − 4( )
Example 1: Identifying Parallel Lines
e. m=___
m=___
m=___
m=___
5-8 Slopes of Parallel and Perpendicular Lines
Identify which lines are parallel or perpendicular.
1. y = −4
2. y− 6 = 5 x + 4( )
3. x = 3
4. y = 15x + 2
Example 1: Identifying Parallel Lines
f. m=___
m=___
m=___
m=___
5-8 Slopes of Parallel and Perpendicular Lines
Example 5: Writing Equations of Parallel and Perpendicular Lines
Write two equations, one parallel and one perpendicular to the given line that passes through the point.
A. (4, 10); y = 3x + 8
5-8 Slopes of Parallel and Perpendicular Lines
Example 5: Writing Equations of Parallel and Perpendicular Lines
B. (2, -1); y = 2x - 5
Write two equations, one parallel and one perpendicular, to the given line that passes through the point.
5-8 Slopes of Parallel and Perpendicular Lines
Example 5: Writing Equations of Parallel and Perpendicular Lines
C. (6, 9); y = x - 5
Write two equations, one parallel and one perpendicular, to the given line that passes through the point.
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5-8 Slopes of Parallel and Perpendicular Lines
Example 5: Writing Equations of Parallel and Perpendicular Lines
a. (-5, 15); y = 5x
Write two equations, one parallel and one perpendicular to the given line that passes through the point.
b. (3, 12); y = 3x - 1
c. (20, 40); y = x - 6 45
d. (10, 5); y = 5x + 10
5-8 Slopes of Parallel and Perpendicular Lines
Lesson Quiz: Part I
Write an equation is slope-intercept form for the line described. 1. contains the point (8, –12) and is parallel to
2. contains the point (4, –3) and is perpendicular to
y = 4x + 5