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### Parallel Lines and Perpendicular Lines

- Parallel lines are two lines in the same plane that do not intersect. Two non-vertical lines are parallel if and only if they have the same slope.
- If you are given the equation of a line and a point not on that line, you can find the equation of the line through this point parallel to the given line by using the point-slope form.
- Perpendicular lines are lines that intersect at right angles. Two non-vertical lines are perpendicular if and only if the product of their slopes is –1 (or, equivalently, their slopes are negative reciprocals of each other).
- You can use this fact to determine whether a pairs of lines whose equations have been given are perpendicular or not.
- If you are given the equation of a line and a point, you can find the equation of the line through this point perpendicular to the given line by using the point-slope form. You must first find the slope of the given line and then take its negative reciprocal.

### Parallel Lines and Perpendicular Lines

A line is parallel to the line whose equation is

y = − [1/4]x − 3

This line also passes through the point ( - 5,7)

Find the equation of this line in slop intercept form.

y = − [1/4]x − 3

This line also passes through the point ( - 5,7)

Find the equation of this line in slop intercept form.

- y = mx + b

parallel lines have the same slope

m = − [1/4]b = ? - 7 = − [1/4]( − 5) + b
- 7 = [5/4] + b
- 7 = 1[1/4] + b
- 5[3/4] = b

y = − [1/4]x + 5[3/4]

A line is parallel to the line whose equation is

y = − [3/7]x + 6

This line also passes through the point ( - 4,2)

Find the equation of this line in slop intercept form.

y = − [3/7]x + 6

This line also passes through the point ( - 4,2)

Find the equation of this line in slop intercept form.

- y = mx + b

parallel lines have the same slope

m = − [3/7]b = ? - 2 = − [3/7]( − 4) + b
- 2 = [12/7] + b
- 2 = 1[5/7] + b
- [2/7] = b

y = - [3/7]x + [2/7]

Are the lines determined by the equations

3x − 6y = 18

4x − 2y = 12

parallel, perpendicular, or neither?

3x − 6y = 18

4x − 2y = 12

parallel, perpendicular, or neither?

- 3x − 6y = 18
- − 6y = 18 − 3x
- y = [(18 − 3x)/( − 6)]
- y = [18/( − 6)] − [3x/( − 6)]
- y = − 3 + [x/2]m = [1/2]
- 4x − 2y = 12
- − 2y = − 4x + 12
- y = [( − 4x + 12)/( − 2)]
- y = 2x − 6m = 2
- ([1/2]) ≠ − 1
- ([1/2]) ≠ (2)

neither

Are the lines determined by the equations

5x − 2y = 10

2x + 12y = 24

parallel, perpendicular, or neither?

5x − 2y = 10

2x + 12y = 24

parallel, perpendicular, or neither?

- 5x − 2y = 10
- − 2y = − 5x + 10
- y = [( − 5x)/( − 2)] + [10/( − 2)]
- y = [5/2]x − 5m = [5/2]
- 2x + 12y = 24
- 12y = − 2x + 24
- y = [( − 2x)/12] + [24/12]
- y = − [x/6] + 2m = − [1/6]
- (−[1/6])([5/2]) ≠ − 1
- (−[1/6]) ≠ ([5/2])

neither

A line passes through the point ( - 4, - 3) and is perpendicular to the line whose equation is y = 1/5 x − 6. Find the equation of this line in slope intercept form.

- y = mx + b

m = [1/5]

negative reciprocal = - 5 - − 3 = − 5( − 4) + b
- − 3 = 20 + b
- − 23 = b

y = − 5x − 23

A line passes through the point (5,4) and is perpendicular to the line whose equation is y = − 7/10 x + 3. Find the equation of this line in slope intercept form.

- y = mx + b

m = − [7/10]

negative reciprocal = [10/7] - 4 = [10/7](5) + b
- 4 = [50/7] + b
- 4 = 7[1/7] + b
- - 3[1/7] = b

y = [10/7]x − 3[1/7]

A line is perpendicular to the line whose equation is 2x − 4y = 8. This line also passes through the y - intercept of the graph of x − 5y = 20. Find the equation of this line in slope intercept form.

- 2x − 4y = 8
- − 4y = − 2x + 8
- y = [( − 2x + 8)/( − 4)]
- y = [1/2]x − 2
- m = [1/2]

slope of perpendicular line = - 2 - x − 5y = 20
- − 5y = − x + 20
- y = [( − x + 20)/( − 5)]
- y = [1/5]x − 4b = − 4

y = − 2x + 4

A line is perpendicular to the line whose equation is 3x − 7y = 42. This line also passes through the y - intercept of the graph of 6x + 3y = 30. Find the equation of this line in slope intercept form.

- 3x − 7y = 42
- − 7y = − 3x + 42
- y = [( − 3x + 42)/( − 7)]
- y = [3/7]x − 6

negative reciprocal = − [7/3] - 6x + 3y = 30
- 3y = − 6x + 30
- y = [( − 6x + 30)/3]
- y = − 2x + 10

b = 10

y = − [7/3]x + 10

A line is parallel to the line whose equation is

y = − [2/5]x − 6

This line also passes through the point ( - 10,12)

Find the equation of this line in slop intercept form.

y = − [2/5]x − 6

This line also passes through the point ( - 10,12)

Find the equation of this line in slop intercept form.

- y = mx + b

parallel lines have the same slope

m = − [2/5]b = ? - 12 = − [2/5]( − 10) + b
- 12 = [20/5] + b
- 12 = 4 + b
- 16 = b

y = − [2/5]x + 16

A line passes through the point ( - 6, - 4) and is perpendicular to the line whose equation is y = − 2/3 x + 8. Find the equation of this line in slope intercept form.

- m = − [2/3]

negative reciprocal = [3/2] - − 4 = [3/2]( − 6) + b
- − 4 = [( − 18)/2] + b
- − 4 = − 9 + b
- 5 = b

y = [3/2]x + 5

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Parallel Lines and Perpendicular Lines

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Parallel Lines 0:08
- Example
- Vertical Lines
- Perpendicular Lines 1:19
- Negative Reciprocal
- Example
- Example 1: Slope Intercept Form 3:25
- Example 2: Parallel or Perpendicular 6:15
- Example 3: Slope Intercept Form 9:27
- Example 4: Slope Intercept Form 12:35

3 answers

Last reply by: Dr Carleen Eaton

Sat Sep 14, 2013 2:39 PM

Post by leo leyva on July 16, 2013

i think at minute 14:20 in the equation on the step -8y=-3/-8(x)+2/-8 you simplified wrong the slope... you didnt turn it into a negative you left it as a positive. or am i wrong? sincerely confused)