Card 1 of 20
EasyStudy card 1
Prompt
What slope relationship identifies parallel nonvertical lines?
Distinct parallel lines have different intercepts.
Answer
They have equal slopes.
Example
Slope 3 is parallel to slope 3.
MathChapter 3: Functions and Linear Equations
Flashcards
Parallel and Perpendicular Lines Flashcards
Twenty original recall cards covering 3-4 parallel and perpendicular lines concepts, procedures, graphs, and traps.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What slope relationship identifies perpendicular nonvertical lines?
Both must be defined and nonzero.
Answer
Their slopes are negative reciprocals and multiply to -1.
Example
\((2/3)(-3/2)=-1\).
Card 3 of 20
EasyStudy card 3
Prompt
What is the perpendicular slope to 2/3?
Reciprocal plus sign change.
Answer
\(-3/2\).
Example
Do not answer \(3/2\).
Card 4 of 20
EasyStudy card 4
Prompt
What is the perpendicular slope to -4?
Write \(-4=-4/1\).
Answer
\(1/4\).
Example
The product \((-4)(1/4)=-1\).
Card 5 of 20
MediumStudy card 5
Prompt
What are all distinct vertical lines to one another?
They share undefined slope.
Answer
Parallel.
Example
\(x=-2\) and \(x=5\) never meet.
Card 6 of 20
MediumStudy card 6
Prompt
What are all distinct horizontal lines to one another?
They all have slope zero.
Answer
Parallel.
Example
\(y=1\) and \(y=-3\) never meet.
Card 7 of 20
MediumStudy card 7
Prompt
How are a vertical and horizontal line related?
They meet at a right angle.
Answer
Perpendicular.
Example
\(x=2\) is perpendicular to \(y=5\).
Card 8 of 20
MediumStudy card 8
Prompt
What is the first step in writing a parallel line through a point?
Then use point-slope form.
Answer
Find the original slope and keep it unchanged.
Example
Do not keep the original intercept unless the same line is intended.
Card 9 of 20
MediumStudy card 9
Prompt
What is the first step in writing a perpendicular line through a point?
Then use the new point.
Answer
Find the original slope, then take its negative reciprocal.
Example
Separate slope conversion from point substitution.
Card 10 of 20
MediumStudy card 10
Prompt
Why is 'flip the fraction' incomplete advice?
Reciprocal alone is not enough.
Answer
Perpendicular slopes also require a sign change.
Example
\(3/5\) becomes \(-5/3\).
Card 11 of 20
MediumStudy card 11
Prompt
How do you classify lines in standard form?
Special-case vertical lines.
Answer
Solve each equation for y, then compare slopes and intercepts.
Example
Do not compare raw x-coefficients alone.
Card 12 of 20
MediumStudy card 12
Prompt
What if two line equations have the same slope and same intercept?
Every point is shared.
Answer
They are the same coincident line, not distinct parallel lines.
Example
Simplify before classifying.
Card 13 of 20
MediumStudy card 13
Prompt
What if slopes are equal but intercepts differ?
They have no intersection.
Answer
The lines are distinct and parallel.
Example
This also describes a no-solution system.
Card 14 of 20
MediumStudy card 14
Prompt
How can a missing coordinate be found from parallelism?
Solve the resulting equation.
Answer
Set the segment's coordinate slope equal to the known line's slope.
Example
Use matching subtraction order.
Card 15 of 20
MediumStudy card 15
Prompt
How can a missing coordinate be found from perpendicularity?
Convert slope first.
Answer
Set the segment slope equal to the negative reciprocal of the known slope.
Example
Then solve for the coordinate.
Card 16 of 20
MediumStudy card 16
Prompt
What product checks perpendicular defined nonzero slopes?
It is a fast verification.
Answer
\(m_1m_2=-1\).
Example
A product of \(1\) does not indicate perpendicularity.
Card 17 of 20
MediumStudy card 17
Prompt
Can two lines with slopes 2 and -2 be perpendicular?
Negative signs alone are insufficient.
Answer
No. Their product is -4, not -1.
Example
The perpendicular to 2 is \(-1/2\).
Card 18 of 20
MediumStudy card 18
Prompt
Can parallel lines have different equations?
Equation appearance may vary by form.
Answer
Yes. Their slopes match while intercepts differ.
Example
Convert both to comparable form.
Card 19 of 20
MediumStudy card 19
Prompt
What line through (a,b) is vertical?
Its y-coordinate can vary.
Answer
\(x=a\).
Example
No slope-intercept form represents a vertical line.
Card 20 of 20
MediumStudy card 20
Prompt
What line through (a,b) is horizontal?
Its slope is zero.
Answer
\(y=b\).
Example
The x-coordinate can vary.
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