1. 5.5: Writing Equations of Parallel and Perpendicular Lines
Do NOW
Write the following as an equation in point-slope form
(7, –1), m = –6
(–6, 6), m = 3/2
(–4, –1), (6, –7)
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5.5: Writing Equations of Parallel and Perpendicular Lines

2. 5.5: Writing Equations of Parallel and Perpendicular Lines
Worksheet Key
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5.5: Writing Equations of Parallel and Perpendicular Lines

3. Parallel & Perpendicular Lines
Section 5.5
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5.5: Writing Equations of Parallel and Perpendicular Lines

4. 5.5: Writing Equations of Parallel and Perpendicular Lines
Definitions
Linear equation: An equation whose graph is a line Slope is a non-vertical line of the vertical change to the horizontal change between two points of a line Y-intercept is where the line crosses the y-axis
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5.5: Writing Equations of Parallel and Perpendicular Lines

5. 5.5: Writing Equations of Parallel and Perpendicular Lines
Slope Equation:
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5.5: Writing Equations of Parallel and Perpendicular Lines

6. 5.5: Writing Equations of Parallel and Perpendicular Lines
Recall
Slope
Y-intercept
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5.5: Writing Equations of Parallel and Perpendicular Lines

7. 5.5: Writing Equations of Parallel and Perpendicular Lines
Steps
Determine the first line of the slopes by putting it in Slope-Intercept form
Determine the second line of the slopes
Compare the slopes and determine whether is parallel, perpendicular, or neither slopes
Parallel Slopes: SAME SLOPE
Perpendicular Slopes: OPPOSITE SIGN RECIPROCAL SLOPE
Neither Slopes: Does not fit either A or B
PARALLEL Slopes
PERPENDICULAR Slopes
PARA||EL
PERPEND CULAR
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5.5: Writing Equations of Parallel and Perpendicular Lines 7

8. 5.5: Writing Equations of Parallel and Perpendicular Lines
Parallel Lines
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5.5: Writing Equations of Parallel and Perpendicular Lines 8

9. 5.5: Writing Equations of Parallel and Perpendicular Lines
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5.5: Writing Equations of Parallel and Perpendicular Lines 9

10. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 1
Line 1 contains points of (4, –1) and (7, –2)
Line 2 contains points of (–2, 1) and (1, 0)
Is it parallel, perpendicular, or neither? x y 4 –1 7 –2 x y –2 1
Parallel
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5.5: Writing Equations of Parallel and Perpendicular Lines

11. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 2
Line 1 contains points of (1, 4) and (2, 7)
Line 2 contains points of (1, 0) and (–2, 1)
Is it parallel, perpendicular, or neither? x y 1 4 2 7 x y 1 –2
Perpendicular
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5.5: Writing Equations of Parallel and Perpendicular Lines

12. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 3
Line 1 contains points of (–4, –8) and (0, –6)
Line 2 contains points of (0, 2) and (1, 4)
Is it parallel, perpendicular, or neither? x y –4 –8 –6 x y 2 1 4
Neither
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5.5: Writing Equations of Parallel and Perpendicular Lines

13. 5.5: Writing Equations of Parallel and Perpendicular Lines
Your Turn
Line 1 contains points of (4, 3) and (3, –1)
Line 2 contains points of (–3, 3) and (1, 2)
Is it parallel, perpendicular, or neither?
Perpendicular
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5.5: Writing Equations of Parallel and Perpendicular Lines

14. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 4
Determine whether the lines are parallel, perpendicular, or neither of
Perpendicular
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15. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 5
Determine whether the lines are parallel, perpendicular, or neither of
Parallel
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16. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 6
Determine whether the lines are parallel, perpendicular, or neither of
Parallel
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17. 5.5: Writing Equations of Parallel and Perpendicular Lines
Your Turn
Determine whether the lines are parallel, perpendicular, or neither of
Neither
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5.5: Writing Equations of Parallel and Perpendicular Lines 17

18. Given Point and Equation
Rewrite the equation in Slope Intercept form
Apply the appropriate slope
Plug in points (x and y) and solve for the y-intercept
Simplify
Check using the Graphing Calculator
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5.5: Writing Equations of Parallel and Perpendicular Lines

19. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 7
Write an equation of a line that contains the point (2, –3) and is parallel to the line y = –2x + 8 in slope-intercept form.
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5.5: Writing Equations of Parallel and Perpendicular Lines

20. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 8
Write an equation of a line that contains the point (2, –3) and is perpendicular to the line y = –2x + 8 in slope-intercept form.
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5.5: Writing Equations of Parallel and Perpendicular Lines

21. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 9
Write an equation of a line that contains the point (3, –3) and is parallel to the line y = x + 5 in slope-intercept form.
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5.5: Writing Equations of Parallel and Perpendicular Lines

22. 5.5: Writing Equations of Parallel and Perpendicular Lines
Your Turn
Write an equation of a line that contains the point (3, –3) and is perpendicular to the line y = x + 5 in slope-intercept form.
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5.5: Writing Equations of Parallel and Perpendicular Lines

23. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 10
Write an equation of a line that is parallel to the line x = 5 and contains the point of (4, 2)
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5.5: Writing Equations of Parallel and Perpendicular Lines

24. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 11
Write an equation of a line that is perpendicular to the line x = 5 and contains the point of (4, 2)
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5.5: Writing Equations of Parallel and Perpendicular Lines

25. 5.5: Writing Equations of Parallel and Perpendicular Lines
Example 12
Write an equation of a line that is parallel to the line y = 5 and contains the point of (4, 2)
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5.5: Writing Equations of Parallel and Perpendicular Lines

26. 5.5: Writing Equations of Parallel and Perpendicular Lines
Your Turn
Write an equation of a line that is perpendicular to the line y = 5 and contains the point of (4, 2)
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5.5: Writing Equations of Parallel and Perpendicular Lines

27. 5.5: Writing Equations of Parallel and Perpendicular Lines
Assignment
Worksheet
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5.5: Writing Equations of Parallel and Perpendicular Lines