Parallel and Perpendicular Lines

Show your work for each problem.

1.
Which pair of lines is parallel?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
Both lines have slope , so they are parallel. The different y-intercepts ( and ) confirm they are distinct parallel lines.
2.
Which pair of lines is perpendicular?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
The slopes are and . Since , the lines are perpendicular.
3.
What is the slope of a line parallel to ?
Answer: 5
The slope of is . Parallel lines have the same slope, so the answer is .
4.
What is the slope of a line perpendicular to ?
Answer: -1/4
The slope is . The negative reciprocal is .
5.
The lines and are:
1. a)Parallel
2. b)Neither parallel nor perpendicular
3. c)The same line
4. d)Perpendicular
Answer: Perpendicular
The slopes are and . Since , the lines are perpendicular.
6.
What is the slope of a line perpendicular to ?
Answer: 3/2
The slope is . The negative reciprocal is .
7.
Write the equation of a line parallel to that passes through .
Answer: y = 3x + 4
1. What is the slope of the given line? 3
2. What slope should the parallel line have? 3
3. Using point-slope form , what is the y-intercept? 4
8.
Write the equation of a line perpendicular to that passes through .
Answer: y = -1/2x + 3
1. What is the slope of the given line? 2
2. What is the negative reciprocal of ? -1/2
3. Using point-slope form with and , what is the y-intercept? 3
9.
What is the relationship between and ?
1. a)Perpendicular
2. b)Same line
3. c)Neither
4. d)Parallel
Answer: Parallel
First equation: . Second equation: . Same slope (), different y-intercepts, so parallel.
10.
Line passes through and . Line is perpendicular to Line . What is the slope of Line ?
Answer: -1/2
Slope of : . Perpendicular slope: .
11.
Find the equation of a line through perpendicular to .
Answer: y = 4x + 11
1. What is the slope of the given line? -1/4
2. What is the negative reciprocal of ? 4
3. Using , simplify to find the equation. y = 4x + 11
12.
Line has equation . Find the equation of line that is perpendicular to and passes through .
Answer: y = 5/2x - 27/2
1. Convert to slope-intercept form. What is the slope? -2/5
2. What is the perpendicular slope? 5/2
3. Using point-slope with and , what is the equation? y = 5/2x - 27/2
13.
Which value of makes the lines and perpendicular?
1. a)
2. b)
3. c)
4. d)
Answer:
For perpendicular lines: , so .
14.
A line parallel to passes through . What is the y-intercept of this line?
Answer: 10
Parallel slope: . Using : , so . Y-intercept is .
15.
Find the equation of the line through that is parallel to the line through and .
Answer: y = -3/2x + 13/2
1. Find the slope of the line through and . -3/2
2. What slope does the parallel line have? -3/2
3. Using and , find the equation. y = -3/2x + 13/2
16.
If two lines are perpendicular and one has slope , what is the slope of the other?
Answer: 1
The negative reciprocal of is .
17.
Determine if the triangle with vertices , , and has a right angle.
Answer: Yes
1. What is the slope of side ? 0
2. What is the slope of side ? undefined
3. Are horizontal and vertical lines perpendicular? yes
18.
The lines and are perpendicular. What is the value of ?
1. a)
2. b)
3. c)
4. d)
Answer:
First line: , slope . Second line: , slope . For perpendicular: , so , giving .