Question 1(Multiple Choice Worth 1 points)

(05.05 LC)

Write an inequality to represent the graph.

a solid line passing through points 0 comma negative 7 and 3 comma negative 5 with shading above the line

y is greater or equal to than two thirds times x minus 7
y is less than or equal to two thirds times x minus 7
y is greater than or equal to three halves times x minus 7
y is less than or equal to three halves times x minus 7
Question 2(Multiple Choice Worth 1 points)
(05.05 MC)

Which of the following inequalities matches the graph?

graph of an inequality with a solid line through the points 1, 4 and 2, 9 with shading below the line

The correct inequality is not listed.
5x + y ≥ 1
5x + y ≤ 1
5x − y ≥ 1
Question 3(Multiple Choice Worth 1 points)
(05.05 MC)

Determine if the ordered pair (6, 4) is a solution to the inequality y is less than three fourths times x minus 3.

No, because (6, 4) is above the line
Yes, because (6, 4) is below the line
Yes, because (6, 4) is on the line
No, because (6, 4) is on the line
Question 4(Multiple Choice Worth 1 points)
(05.05 LC)

Which of the following inequalities matches the graph?

graph of an inequality with a dashed horizontal line through the point 0, 4 and shading below the line

x > 4
x < 4
y > 4
y < 4
Question 5(Multiple Choice Worth 1 points)
(05.05 MC)

Lincoln Middle School has a total of $200 to spend on notebooks and tablets for the school board meeting. Notebooks cost $7 each, and tablets cost $5 each.

If x represents the number of notebooks and y represents the number of tablets, which graph correctly shows the solution to the problem 7x + 5y ≤ 200?

X, Y graph. X range is negative 60 to 60, and y range is negative 60 to 60. Solid line on graph has negative slope and runs through 0, 40 and 50, negative 30. Below line is shaded.
X, Y graph. X range is negative 60 to 44, and y range is negative 60 to 60. Solid line on graph has negative slope and runs through 0, 40 and 50, negative 30. Above line is shaded.
X, Y graph. X range is negative 60 to 44, and y range is negative 60 to 60. Dashed line on graph has negative slope and runs through 0, 40 and 50, negative 30. Above line is shaded.
X, Y graph. X range is negative 60 to 44, and y range is negative 60 to 60. Dashed line on graph has negative slope and runs through 0, 40 and 50, negative 30. Below line is shaded.
Question 6(Multiple Choice Worth 1 points)
(05.05 MC)

The networking organization you joined is throwing a party. You are in charge of buying the chips, which cost $2.50 per bag, and salsa, which costs $4 per jar. The chips and salsa budget you are given totals $60. The inequality 2.5x + 4y ≤ 60 represents the possible combinations of chips (x) and salsa (y) you can buy.

The graph shows a solid line with an x-intercept at 24, a y-intercept at 15, and shading below the line.

Which of the following does not represent a solution to the inequality?

10 bags of chips and 2 jars of salsa
20 bags of chips and 2 jars of salsa
14 bags of chips and 5 jars of salsa
18 bags of chips and 6 jars of salsa
Question 7(Multiple Choice Worth 1 points)
(05.05 LC)

Which correctly describes how the graph of the inequality −4y − x ≥ 7 is shaded?

Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
Question 8(Multiple Choice Worth 1 points)
(05.05 LC)

Which of the following inequalities matches the graph?

graph of an inequality with a dashed vertical line through the point negative 3, 0 with shading to the left of the line

x > −3
x < −3
y > −3
y < −3
Question 9(Multiple Choice Worth 1 points)
(05.05 MC)

In which quadrants do solutions for the inequality y is less than or equal to two sevenths times x plus 1 exist?

I, III, and IV
I, II, and III
I and IV
All four quadrants
Question 10(Multiple Choice Worth 1 points)
(05.05 MC)

Which inequality matches the graph?

X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Solid line on graph has positive slope and runs through negative 9, negative 10 and negative 3, negative 1 and 3, 8. Above line is shaded.

−2x + 3y > 7
2x − 3y < 7
−3x + 2y ≥ 7
3x − 2y ≤ 7

1 answer

Here are the answers to the multiple-choice questions you provided:

Question 1:
The line passes through (0, -7) and (3, -5). The slope (m) can be calculated as: \[ m = \frac{-5 - (-7)}{3 - 0} = \frac{2}{3} \] The equation of the line is in the form: \[ y = \frac{2}{3} x - 7 \]

Since the shading is above the line and there is a solid line, the correct inequality is: Answer: y ≥ (2/3)x - 7


Question 2:
The equation of the line can be determined from the points (1, 4) and (2, 9). The slope (m) is: \[ m = \frac{9 - 4}{2 - 1} = 5 \] The equation of the line can be written as: \[ y - 4 = 5(x - 1) \] or \[ y = 5x - 1 \] Since the shading is below the line, we consider the inequality: Answer: 5x + y ≤ 1


Question 3:
For the inequality \( y < \frac{3}{4}x - 3 \): Substituting \( x = 6 \): \[ y < \frac{3}{4} \cdot 6 - 3 = \frac{18}{4} - 3 = 4.5 - 3 = 1.5 \] Since 4 is greater than 1.5, the point (6, 4) is above the line. Answer: No, because (6, 4) is above the line


Question 4:
A dashed horizontal line through (0, 4) indicates that y cannot be equal to 4, and since the shading is below the line: Answer: y < 4


Question 5:
The maximum y-intercept occurs when \( x = 0 \): \[ 7(0) + 5y ≤ 200 \rightarrow y ≤ 40 \] The maximum x-intercept occurs when \( y = 0 \): \[ 7x + 5(0) ≤ 200 \rightarrow x ≤ \frac{200}{7} \approx 28.57 \] The inequality indicates that the area below the line is shaded. Answer: X, Y graph. X range is negative 60 to 44... Below line is shaded.


Question 6:
For the inequality \( 2.5x + 4y ≤ 60 \):

  • For 10 bags of chips and 2 jars of salsa: \[ 2.5(10) + 4(2) = 25 + 8 = 33 ≤ 60\]
  • For 20 bags of chips and 2 jars of salsa: \[ 2.5(20) + 4(2) = 50 + 8 = 58 ≤ 60\]
  • For 14 bags of chips and 5 jars of salsa: \[ 2.5(14) + 4(5) = 35 + 20 = 55 ≤ 60\]
  • For 18 bags of chips and 6 jars of salsa: \[ 2.5(18) + 4(6) = 45 + 24 = 69 > 60\] Thus, this is not a solution. Answer: 18 bags of chips and 6 jars of salsa

Question 7:
The inequality \(-4y - x ≥ 7\) can be rewritten as: \[ -4y \geq x + 7 \] or \[ y \leq -\frac{1}{4}x - \frac{7}{4} \] This indicates shading below the line (solid line). Answer: Below the solid line


Question 8:
A dashed vertical line through \((-3, 0)\) with shading to the left indicates: Answer: x < −3


Question 9:
The inequality \( y ≤ \frac{2}{7}x + 1 \) intersects the y-axis at 1 and has a positive slope, meaning it will be true in quadrants I and III (below and including the line). Answer: I and IV


Question 10:
The line has a positive slope and the shading is above the line. The equation can be manipulated to determine the matching inequality: Answer: 3x − 2y ≤ 7


Let me know if you have any more questions!