1.
Which point is a solution of the inequality y > 2x + 3
Correct Answer
D. (–3, 6)
Explanation
The point (–3, 6) is a solution to the inequality y > 2x + 3 because when we substitute x = –3 and y = 6 into the inequality, we get 6 > 2(-3) + 3, which simplifies to 6 > -6 + 3, and further simplifies to 6 > -3. Since 6 is indeed greater than -3, the point (–3, 6) satisfies the inequality.
2.
Which point is NOT a solution of the inequality y < –x + 3
Correct Answer
C. (4, –1)
Explanation
The point (4, -1) is not a solution of the inequality y < -x + 3 because when we substitute the values of x = 4 and y = -1 into the inequality, we get -1 < -4 + 3, which simplifies to -1 < -1. Since this statement is not true, the point (4, -1) is not a solution.
3.
Which inequality is best represented by the graph below?
Correct Answer
A.
4.
Which inequality is best represented by the graph below?
Correct Answer
E. Not here
Explanation
correct answer:
5.
Which inequality is represented by the graph below?
Correct Answer
C.
6.
Which of the following describes the graph of ?
Correct Answer
C. The boundary line is solid, and the shading is to the right.
Explanation
The graph described in the answer choice means that the boundary line is a solid line and the shading is on the right side of the line. This indicates that the solution to the inequality represented by the graph is all the points on the right side of the line, including the line itself.
7.
Which of the following describes the graph of y > –2x + 5?
Correct Answer
A. The boundary line is dashed, and the shading is above the line.
Explanation
The given inequality is y > -2x + 5. In this case, the boundary line is represented by y = -2x + 5. Since the inequality is a strict inequality (y >), the boundary line is dashed. The shading is above the line because the solution set consists of all the points that are greater than the y-values on the line.
8.
Which of the following describes the graph of y < –4?
Correct Answer
B. The boundary line is dashed, and the shading is below.
Explanation
The inequality y < -4 represents all the points on the coordinate plane that have a y-coordinate less than -4. Since the boundary line is dashed, it means that the points on the line itself are not included in the solution. The shading being below the line indicates that the region below the line, or the area where the y-coordinate is less than -4, is the solution to the inequality. Therefore, the correct answer is "The boundary line is dashed, and the shading is below."
9.
Tell whether the ordered pair is a solution of the given system.
Correct Answer
A. Yes
Explanation
The explanation for the given correct answer is not available as the question and options provided are incomplete and unclear.
10.
Tell whether the ordered pair is a solution of the given system.
Correct Answer
B. No
Explanation
The given answer "no" indicates that the ordered pair is not a solution of the given system. However, without the context of the system or any additional information, it is not possible to provide a specific explanation for why the ordered pair is not a solution.
11.
Write a system of linear inequalities to represent the graph below.
Correct Answer
A.
12.
Write a system of linear inequalities to represent the graph below.
Correct Answer
D. Not here
13.
Write a system of linear inequalities to represent the graph below.
Correct Answer
C.
14.
Which point is a solution of the inequality ?
Correct Answer
C. (6, –2)
Explanation
The point (6, -2) is a solution of the inequality because when we substitute the x-coordinate (6) and the y-coordinate (-2) into the inequality, it satisfies the inequality.
15.
Which point is a solution of the inequality 3x – 2y < –10
Correct Answer
A. (–4, 2)
Explanation
The point (–4, 2) is a solution of the inequality 3x – 2y < –10 because when we substitute x = –4 and y = 2 into the inequality, we get 3(-4) – 2(2) = –12 – 4 = –16, which is less than –10. Therefore, the point (–4, 2) satisfies the inequality.
16.
Linda works at a pharmacy for $15 an hour. She also baby-sits for $10 an hour. Linda needs to earn at least $90 per week, but she does not want to work more than 20 hours per week. Write a systems of linear inequalities that could be used to describe the number of hours Linda could work at each job to meet her goals.
Correct Answer
C.
Explanation
Let x be the number of hours Linda works at the pharmacy and y be the number of hours she babysits. The total amount of money she earns from the pharmacy is 15x and from babysitting is 10y. To meet her goal of earning at least $90 per week, the inequality is 15x + 10y ≥ 90. To ensure she does not work more than 20 hours per week, the inequality is x + y ≤ 20. Therefore, the system of linear inequalities is 15x + 10y ≥ 90 and x + y ≤ 20.
17.
What must be true of the boundary lines in a system of two linear inequalities if there is no solution of the system?
Correct Answer
A. The boundary lines must be parallel.
Explanation
If there is no solution to a system of two linear inequalities, it means that the two inequalities do not intersect or overlap. In order for two lines to not intersect, they must be parallel to each other. Therefore, the correct answer is that the boundary lines must be parallel.
18.
Which graph represents the solutions to the given system?
Correct Answer
A.
19.
What is the solution to the system of equations graphed below?
Correct Answer
D. (3, 2)
Explanation
The solution to the system of equations graphed below is (3, 2). This is the point where the two lines intersect. The coordinates (3, 2) satisfy both equations simultaneously, making it the solution to the system.