Card 1 of 20
EasyStudy card 1
Prompt
What is the boundary line of a linear inequality?
It separates two half-planes.
Answer
The line found by replacing the inequality operator with equality.
Example
For \(y>2x-1\), the boundary is \(y=2x-1\).
MathChapter 4: Linear Inequalities and Graphs
Flashcards
Graphing Inequalities in Two Variables Flashcards
Twenty retrieval cards for boundaries, line styles, test points, shading, and graph interpretation.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
When is a boundary dashed?
Equality is excluded.
Answer
For strict inequalities \(<\) or \(>\).
Example
Use dashed for \(y<3x+2\).
Card 3 of 20
EasyStudy card 3
Prompt
When is a boundary solid?
Equality is allowed.
Answer
For inclusive inequalities \(\le\) or \(\ge\).
Example
Use solid for \(y\ge-x\).
Card 4 of 20
EasyStudy card 4
Prompt
What is a half-plane?
An inequality selects one side.
Answer
One of the two regions separated by a line.
Example
Every point above \(y=2\) forms one half-plane.
Card 5 of 20
EasyStudy card 5
Prompt
What is a solution point to a two-variable inequality?
Substitute x and y.
Answer
An ordered pair that makes the inequality true.
Example
\((1,3)\) satisfies \(y>x\).
Card 6 of 20
MediumStudy card 6
Prompt
What is the safest way to choose shading?
The origin is convenient, not mandatory.
Answer
Test a point not on the boundary in the original inequality.
Example
If \((0,0)\) works, shade its side.
Card 7 of 20
MediumStudy card 7
Prompt
Why should a test point not lie on the boundary?
Choose an off-line point.
Answer
It only produces equality and cannot identify the valid side.
Example
If the line passes through the origin, test \((1,0)\).
Card 8 of 20
MediumStudy card 8
Prompt
What does shading above \(y=mx+b\) indicate?
Above means larger y.
Answer
Y-values greater than the boundary output.
Example
Dashed above gives \(y>mx+b\).
Card 9 of 20
MediumStudy card 9
Prompt
What does shading below \(y=mx+b\) indicate?
Below means smaller y.
Answer
Y-values less than the boundary output.
Example
Solid below gives \(y\le mx+b\).
Card 10 of 20
MediumStudy card 10
Prompt
How do you graph \(x<a\)?
Smaller x-values lie left.
Answer
Use vertical boundary \(x=a\) and shade left.
Example
Use dashed when the operator is strict.
Card 11 of 20
MediumStudy card 11
Prompt
How do you graph \(x\ge a\)?
Larger x-values lie right.
Answer
Use solid vertical boundary \(x=a\) and shade right.
Example
Equality makes the line solid.
Card 12 of 20
MediumStudy card 12
Prompt
How do you graph \(y<b\)?
Smaller y-values lie below.
Answer
Use dashed horizontal boundary \(y=b\) and shade below.
Example
Boundary points are excluded.
Card 13 of 20
MediumStudy card 13
Prompt
How do you graph \(y\ge b\)?
Larger y-values lie above.
Answer
Use solid horizontal boundary \(y=b\) and shade above.
Example
Boundary points are included.
Card 14 of 20
MediumStudy card 14
Prompt
How do you recover an inequality from a graph?
Use three separate clues.
Answer
Find the boundary equation, read solid/dashed inclusion, then determine the shaded side.
Example
Test a shaded point to verify the operator.
Card 15 of 20
MediumStudy card 15
Prompt
What is the boundary for \(2x-y>4\)?
Replace the operator with equality.
Answer
\(2x-y=4\), or \(y=2x-4\).
Example
The strict operator makes this boundary dashed.
Card 16 of 20
MediumStudy card 16
Prompt
Does a solid line determine which side to shade?
Style and shading are separate decisions.
Answer
No. It determines inclusion only; a test point determines the side.
Example
Both \(y\le x\) and \(y\ge x\) use the same solid boundary.
Card 17 of 20
MediumStudy card 17
Prompt
What common error follows solving for \(y\) by dividing by a negative?
Algebra affects shading direction.
Answer
Failing to reverse the inequality direction.
Example
From \(-y<2x\), obtain \(y>-2x\).
Card 18 of 20
MediumStudy card 18
Prompt
What should a graph description communicate?
Make the visual understandable without color.
Answer
Boundary equation, solid/dashed style, and the shaded side or test-point result.
Example
Describe ‘solid line and region below,’ not merely ‘blue graph.’
Card 19 of 20
MediumStudy card 19
Prompt
How can you verify a shaded half-plane?
One should pass and one should fail.
Answer
Test one shaded point and one unshaded point in the original inequality.
Example
Also verify the boundary style separately.
Card 20 of 20
MediumStudy card 20
Prompt
What is the key graphing workflow?
Use a fixed order.
Answer
Boundary, boundary style, off-line test point, then shading.
Example
Do not shade before testing.
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