Practice
Graphing Inequalities in Two Variables Practice
Fifty original questions covering boundaries, test points, half-planes, special lines, and graph interpretation.
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Question 1
Explanation
Equality is included, so the boundary is solid.
Question 2
Explanation
The operator is strict, so the boundary is dashed.
Question 3
Explanation
Equality is included, so the boundary is solid.
Question 4
Explanation
The operator is strict, so the boundary is dashed.
Question 5
Explanation
Equality is included, so the boundary is solid.
Question 6
Explanation
Substituting \((0,0)\) into \(x+y\le4\) gives a true statement, consistent with the shaded side.
Question 7
Explanation
Substituting \((0,0)\) into \(2x-y>2\) gives a false statement, consistent with the unshaded side.
Question 8
Explanation
Substituting \((0,0)\) into \(-x+2y\ge-2\) gives a true statement, consistent with the shaded side.
Question 9
Explanation
Substituting \((0,0)\) into \(3x+y<6\) gives a true statement, consistent with the shaded side.
Question 10
Explanation
Substituting \((0,0)\) into \(x-2y\le4\) gives a true statement, consistent with the shaded side.
Question 11
Explanation
The boundary coefficients, solid style, and below shading together identify \(x+y\le4\).
Question 12
Explanation
The boundary coefficients, dashed style, and below shading together identify \(2x-y>2\).
Question 13
Explanation
The boundary coefficients, solid style, and above shading together identify \(-x+2y\ge-2\).
Question 14
Explanation
The boundary coefficients, dashed style, and below shading together identify \(3x+y<6\).
Question 15
Explanation
The boundary coefficients, solid style, and above shading together identify \(x-2y\le4\).
Question 16
Explanation
A vertical line fixes x and separates left from right. The graph represents \(x<-1\).
Question 17
Explanation
A horizontal line fixes y and separates below from above. The graph represents \(y>=0\).
Question 18
Explanation
A vertical line fixes x and separates left from right. The graph represents \(x>=1\).
Question 19
Explanation
A horizontal line fixes y and separates below from above. The graph represents \(y<2\).
Question 20
Explanation
A vertical line fixes x and separates left from right. The graph represents \(x>=3\).
Question 21
Explanation
Substitution gives \(0<=4\), which is true. Therefore shade that side.
Question 22
Explanation
Substitution gives \(3>2\), which is true. Therefore shade that side.
Question 23
Explanation
Substitution gives \(7>=-2\), which is true. Therefore shade that side.
Question 24
Explanation
Substitution gives \(7<6\), which is false. Therefore do not shade that side.
Question 25
Explanation
Substitution gives \(0<=4\), which is true. Therefore shade that side.
Question 26
Explanation
Replace the operator with equality and solve for \(y\). The exact boundary is \(y=-1x+4\).
Question 27
Explanation
Replace the operator with equality and solve for \(y\). The exact boundary is \(y=2x-2\).
Question 28
Explanation
Replace the operator with equality and solve for \(y\). The exact boundary is \(y=0.5x-1\).
Question 29
Explanation
Replace the operator with equality and solve for \(y\). The exact boundary is \(y=-3x+6\).
Question 30
Explanation
Replace the operator with equality and solve for \(y\). The exact boundary is \(y=0.5x-2\).
Question 31
Explanation
Substitute each candidate. \((0,0)\) makes the inequality true and lies in the shaded region.
Question 32
Explanation
Substitute each candidate. \((2,0)\) makes the inequality true and lies in the shaded region.
Question 33
Explanation
Substitute each candidate. \((0,0)\) makes the inequality true and lies in the shaded region.
Question 34
Explanation
Substitute each candidate. \((0,0)\) makes the inequality true and lies in the shaded region.
Question 35
Explanation
Substitute each candidate. \((0,0)\) makes the inequality true and lies in the shaded region.
Question 36
Explanation
Set \(x=0\) in the boundary equation \(1x+1y=4\). This gives \(y=4\).
Question 37
Explanation
Set \(x=0\) in the boundary equation \(2x+-1y=2\). This gives \(y=-2\).
Question 38
Explanation
Set \(x=0\) in the boundary equation \(-1x+2y=-2\). This gives \(y=-1\).
Question 39
Explanation
Set \(x=0\) in the boundary equation \(3x+1y=6\). This gives \(y=6\).
Question 40
Explanation
Set \(x=0\) in the boundary equation \(1x+-2y=4\). This gives \(y=-2\).
Question 41
Explanation
The verbal limit translates to \(x+y\le4\), which agrees with the displayed boundary and shading.
Question 42
Explanation
The verbal limit translates to \(2x-y>2\), which agrees with the displayed boundary and shading.
Question 43
Explanation
The verbal limit translates to \(-x+2y\ge-2\), which agrees with the displayed boundary and shading.
Question 44
Explanation
The verbal limit translates to \(3x+y<6\), which agrees with the displayed boundary and shading.
Question 45
Explanation
The verbal limit translates to \(x-2y\le4\), which agrees with the displayed boundary and shading.
Question 46
Explanation
The operator includes equality, so a solid boundary is required.
Question 47
Explanation
The operator excludes equality, so a dashed boundary is required.
Question 48
Explanation
The operator includes equality, so a solid boundary is required.
Question 49
Explanation
The operator excludes equality, so a dashed boundary is required.
Question 50
Explanation
The operator includes equality, so a solid boundary is required.
Keyboard: use Tab to move, arrow keys to change answer choices, and Enter to check an answer.
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Questions to review
No mistakes this time. Excellent work.
- Question 1Boundary line styleEasy
- Question 2Boundary line styleEasy
- Question 3Boundary line styleEasy
- Question 4Boundary line styleEasy
- Question 5Boundary line styleEasy
- Question 6Testing solution pointsEasy
- Question 7Testing solution pointsEasy
- Question 8Testing solution pointsEasy
- Question 9Testing solution pointsEasy
- Question 10Testing solution pointsEasy
- Question 11Graph to inequalityEasy
- Question 12Graph to inequalityEasy
- Question 13Graph to inequalityEasy
- Question 14Graph to inequalityEasy
- Question 15Graph to inequalityEasy
- Question 16Vertical and horizontal boundariesMedium
- Question 17Vertical and horizontal boundariesMedium
- Question 18Vertical and horizontal boundariesMedium
- Question 19Vertical and horizontal boundariesMedium
- Question 20Vertical and horizontal boundariesMedium
- Question 21Test-point shadingMedium
- Question 22Test-point shadingMedium
- Question 23Test-point shadingMedium
- Question 24Test-point shadingMedium
- Question 25Test-point shadingMedium
- Question 26Boundary equationMedium
- Question 27Boundary equationMedium
- Question 28Boundary equationMedium
- Question 29Boundary equationMedium
- Question 30Boundary equationMedium
- Question 31Selecting a solution pointMedium
- Question 32Selecting a solution pointMedium
- Question 33Selecting a solution pointMedium
- Question 34Selecting a solution pointMedium
- Question 35Selecting a solution pointMedium
- Question 36Boundary interceptsMedium
- Question 37Boundary interceptsMedium
- Question 38Boundary interceptsMedium
- Question 39Boundary interceptsMedium
- Question 40Boundary interceptsMedium
- Question 41Two-variable modelingHard
- Question 42Two-variable modelingHard
- Question 43Two-variable modelingHard
- Question 44Two-variable modelingHard
- Question 45Two-variable modelingHard
- Question 46Graph error analysisHard
- Question 47Graph error analysisHard
- Question 48Graph error analysisHard
- Question 49Graph error analysisHard
- Question 50Graph error analysisHard