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Coordinate Algebra EOC (GSE) Quiz Answer KeyReasoning with equations and inequalities - (MGSE9‐12.A.REI.12 ) Graph Solutions

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

Which of the points satisfy the linear inequality graphed here?

A) (0, 0)

B) (10, 0)

C) (-10, 0)

D) (10, 10)

Explanation:Solution: (-10, 0).Find a point that lies in the shaded region, or plug the points in and determine which point makes the inequality true.

2)



The graph shown is for the inequality y ≥ x. The graph has one thing wrong. What is it?

A) The shading is on the wrong side of the boundary line.

B) The boundary line should be dotted or dashed

C) The boundary line has the wrong y-intercept

D) The boundary line has the wrong slope

Explanation:Solution: The shading is on the wrong side of the boundary line. To test the shading, pick a test point, plug it in, if it works that areashould be shaded. The test point (0, -10) does not work so the shading is incorrect.

3)

The graph shows the solution to which system of inequalities?

A) y < x + 1 and y < x - 3

B) y ≤ x + 1 and y > x - 3

C) y ≤ x + 1 and y ≤ x - 3

D) y ≤ x + 1 and y ≥ x - 3

Explanation:



The equations in each choice are almost the same. The only difference is the inequality symbol. The solid line in the graphrepresents less than or equal to. The dashed line represents greater than. Therefore the only choice is y ≤ x + 1 and y > x - 3



4)

The graph is supposed to represent this system of inequalities

y > 2

5(x) - 2

y < -3x + 1

What is wrong with the graph?

A) The shaded region is incorrect.

B) The lines graphed should be dashed.

C) The lines are graphed incorrectly.

D) One line should be solid and the other dashed.

Explanation:Check each statement one by one, pick a test point and plug it in to the inequalities and it satisfies both, the lines are graphedcorrectly, but since both inequalitites are not equal to the lines graphed should be dashed.

5)



Which of the inequalities is represented by the graph?

A) y < x + 2

B) y < -x + 2

C) y ≤ -x + 2

D) y ≥ 2x - 1

Explanation:The solution is y < -x + 2. The dotted line indicates that "equal to" is not included in the inequality. Since the y-intercept is 2 and theslope is -1 you know that the solution is B.

6)

Which of the points does NOT satisfy the inequality shaded in the diagram?

A) (4, 0)

B) (0, 0)

C) (-3, -2)

D) (-10, -1)

Explanation:Solution: (4, 0)To determine this answer, determine which point does not lie in the shaded region.

7)



The linear inequality y ≤ 3

2x +

3

2 is graphed. Determine a solution for the inequality.

A) (0, 2)

B) (1, 3)

C) (-2, 0)

D) (-3, 1)

Explanation:The solution is (1,3). Because the line is solid, all points that lie on the line are included. So the point (1, 3) is a solution. The otherpoints do not lie on the line or in the shaded region.



8)

The graph is the boundary line for the inequality y ≤ 2

3x + 1. Which of the points lies in the shaded region for this inequality?

A) (1, 2)

B) (-4, 5)

C) (0, -3)

D) (-10, -2)

Explanation:Solution: (0, -3).To determine the shaded region in a linear inequality you must plug the point in and determine if it makes the inequality true. Thepoint that satisfies the inequality is (0, -3).

9)



y ≤ -1

2x - 3

y ≥ -1

2x + 2

Which area on the graph, if any, represents the solution to the system?

A) A

B) B

C) C

D) No Solution

Explanation:Solution: No SolutionPick a test point from each of the sections, the one point that makes both inequalities true comes from the section that is thesolution. In this case none of the test points make both true, so there is no solution.

10)



Determine a solution for the linear inequality graphed here.

A) (3, 0)

B) (3, -1)

C) (0, 0)

D) (5, 2)

Explanation:The solution is (0, 0). The point (0, 0) falls in the yellow, shaded region of the inequality.

11)



The system of inequalities is partially graphed. The only missing portion is the shading. Which area labeled in the diagram should beshaded to represent the solution?

y ≤ -2

y ≤ xA) A

B) B

C) C

D) D

Explanation:The correct answer is area C. Pick a test point from each area and plug them into each inequality. The point that makes bothinequalities true determines which section is the solution.



12)

Which system of inequalities is represented by the graph?

A)

B)

C)

D)

Explanation:The solution is y ≥ x and y ≤ x + 4. We shade above the line y = x and below the line y = x + 4.

13) What is the set of all points (x, y) that is a solution to the system of inequalities?

2x - 5y > 104x + 6y ≤ 12

x > 0

A) The point (15

4,-

1

2)



B)

C)



D)

Explanation:The correct answer is C. Since there are three equations the shaded region must make all three inequalities true. If you choose testpoint (4, -3) all three inequalities are true so you can shade that region.

14)

The graph shows the solution to which system of inequalities?

A) y < -2x + 4 and y < 2x + 4

B) y < -2x + 4 and y ≤ 2x + 4



C) y > -2x + 4 and y ≤ 2x + 4

D) y ≤ -2x + 4 and y ≤ 2x + 4

Explanation:The equations in each choice are the same. The only difference is the inequality sign. If there is a solid line look for the ≤ sign. If it is

a dotten line, look for the < sign. y < -2x + 4 and y 2x + 4

15)

Which inequality matches the graph shown here?

A) y < x + 2

B) y > x + 2

C) y ≤ x + 2

D) y ≥ x + 2

Explanation:The solution is y ≤ x + 2. The line graphed is y = x + 2. Since the line is solid and the region below the line is shaded we know that ≤is the correct symbol to use.



16)


A) y < 3x - 1

B) y > 3x - 1

C) y ≤ 3x - 1

D) y ≥ 3x - 1

Explanation:The solution is y ≤ 3x - 1. The line graphed is y = 3x - 1. Since the line is solid and the region below the line is shaded we know that≤ is the correct symbol to use.

17)

Which inequality represents the graph?

A) y < x

B) y = x

C) y > x

D) y ≤ x



Explanation:The solution is y ≤ x. The solid line indicates that "equal to" is included in the inequality. Shading below the solid line indicates thatis it "less than or equal to."

18)

Which inequality represents the graph?

A) y < x - 2

B) y > x - 2

C) y ≤ x - 2

D) y ≥ x - 2

Explanation:The solution is y ≥ x - 2. The solid line indicates that "equal to" is included in the inequality. Shading above the solid line indicatesthat it is "greater than or equal to."

19)



The solution set to the system of inequalities is graphed. What is wrong with the graph?

3x - 2y < -5x + 4y > 8

A) The wrong region is shaded.

B) Nothing, the graph is correct.

C) The line(s) are graphed incorrectly.

D) One line should be solid and the other dotted.

Explanation:The correct answer is the wrong region is shaded. If you choose the point (0, 0) in the shaded region the second inequality is notcorrect when you plug it in. Therefore that region should not be shaded.



20)

Which of the statements is true about the graph for the system of inequalities?

y ≤-2x

y ≥ 3A) Area C should be the shaded region.

B) The graph of the boundary line for y ≥ 3 should be dashed.

C) The equations y < -2x should be an uphill line, not a downhill line.

D) Area A should be the shaded region instead of the region shaded on the graph.

Explanation:Solution: Area A should be the shaded region instead of the region shaded on the graph.The entire graph is correct except for the shading area, by picking test points and testing them in the inequalities. When that isdone, the solution should be region A.

21)




A) y < -2x + 4 and y > 3x - 4

B) y > -2x + 4 and y < 3x - 4

C) y ≤ -2x + 4 and y ≥ 3x - 4

D) y ≥ -2x + 4 and y ≤ 3x - 4

Explanation:y < -2x + 4 and y > 3x - 4

We shade above the line for y > 3x - 4 and below the line for y < -2x + 4. The result is the shaded area shown in the graph.

22)

Which system of inequalities is shown in the graph?



A) 2x + 3y ≤ 5 and -3x + 2y < 6

B) 2x + 3y < 5 and -3x + 2y ≤ 6

C) 2x + 3y ≥ 5 and -3x + 2y > 6

D) 2x + 3y > 5 and -3x + 2y ≥ 6

Explanation:This graph is the solution to the system of inequalities 2x + 3y < 5 and -3x + 2y ≤ 6. First find the point of intersection, then shadethe region that makes both inequalities true.

23)


A) y < x + 2

B) y > x + 2

C) y ≤ x + 2

D) y ≥ x + 2

Explanation:The solution is y ≤ x + 2. The line graphed is y = x + 2. Since the line is solid and the region below the line is shaded we know that ≤is the correct symbol to use.



24)

Which of the points listed would fall in the correct shaded area for the inequality? The inequality has been partially graphed in thediagram.

y ≤ 2

3x + 1

A) (0, 2)

B) (0, 0)

C) (-3, 5)

D) (1, 10)

Explanation:Solution; (0, 0).Plug in the above points and find the one point which makes the inequality true. 0 ≤ 0 + 1, so the answer is (0, 0).

25)



The linear inequality y < -2

3x + 2 is graphed. Determine a solution for the inequality.

A) (0, 2)

B) (3, 0)

C) (0, 0)

D) (0, 3)

Explanation:The solution is (0, 0). Because the line is dotted, the points that lie on the line are not included. Only points in the shaded region aresolutions for the inequality. The point (0, 0) lies in the shaded region.

26)



Which system of inequalities is shown in the graph?

A) -3x + y > -2 and 2y > x + 2

B) -3x + y ≥ -2 and 2y ≥ x + 2

C) -3x + y < -2 and 2y < x + 2

D) -3x + y ≤ -2 and 2y ≤ x + 2

Explanation:This graph is the solution to the system of inequalities -3x + y > -2 and 2y > x + 2.

27)

The graph of y ≤ -2x + 4 is shown. Which set contains only points that satisfy the inequality?

A) {(0, 0), (1, 2), (3, -3)}



B) {(0, 0), (1, 2), (7, -2)}

C) {(3, 3), (1, 2), (3, -3)}

D) {(0, 0), (2, 1), (3, -3)}

Explanation:Plot each of the points on the grid. If it falls in the shaded region it satisfies the inequality. The only set of points who ALL satisfythe inequality are {(0, 0), (1, 2), (3, -3)}



28) In which quadrants of the coordinate plane is the shaded region of the inequality located?

y ≤ xA) I, II and III

B) I, II, and IV

C) I, III, and IV

D) II, III, and IV

Explanation:Solution: I, III, and IV. As seen here, the shaded region of the system of inequalities falls in quadrants I III, and IV.

29)




A)

B)

C)

D)

Explanation:The solution is y ≥ x and y ≥ -x. Shading above both y = x and y = -x gives us the graph shown in the picture.

30) The shaded region of the inequality falls in which quadrants?

y ≥ x - 2A) I and II

B) III and IV

C) I, II, III, IV

D) II, III, and IV

Explanation:Solution: I, II, III, IV. As seen here, the graph of the inequality fall in all four quadrants.

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