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Graphical Representation and Interpretation of Inequalities Quiz

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#1

Which of the following is a graphical representation of the inequality x > 3?

A dashed line passing through the point (3,0) with shading on the right side.
Explanation

Dashed line through (3,0), shaded on the right.

#2

For the inequality 2x + y > 8, which point is in the solution set?

(4, 3)
Explanation

Point (4, 3) in solution set.

#3

Which of the following inequalities represents a vertical line when graphed?

x = -5
Explanation

Vertical line: x = -5.

#4

What is the solution set of the inequality 2x + 3y < 12 when graphed?

The area below the line with a slope of -2/3 passing through the points (0,4) and (6,0).
Explanation

Area below line with slope -2/3.

#5

Which of the following inequalities represents a horizontal line when graphed?

y = -5
Explanation

Horizontal line: y = -5.

#6

What does the inequality y ≤ 2x + 1 represent when graphed?

A line passing through the origin with a slope of 2 and shaded area above the line.
Explanation

Line through origin, slope 2, shaded above.

#7

For the inequality 3y - 2x ≥ 6, which region of the graph is shaded when plotted?

Above the line.
Explanation

Shaded area above the line.

#8

What does the shaded area represent in the graphical representation of the inequality y ≥ -3x + 5?

The solution set
Explanation

Shaded area is solution set.

#9

Which of the following inequalities represents a region that includes the origin (0,0) when graphed?

x + y ≤ 3
Explanation

Includes origin in solution.

#10

What is the solution to the inequality system x ≥ -1 and y < 3 when graphed?

A region bounded by the lines x = -1 and y = 3, excluding the boundary lines.
Explanation

Region between x = -1 and y = 3.

#11

In the inequality 4x - 3y > 12, if (2, -4) satisfies the inequality, what does this indicate?

The point lies outside the shaded region.
Explanation

Point lies outside shaded region.

#12

In which quadrant does the solution to the inequality x + y < 4 lie?

Third quadrant
Explanation

Solution in the third quadrant.

#13

What does a dashed boundary line represent in a graphical representation of an inequality?

The line is not a part of the solution set.
Explanation

Dashed line not in solution set.

#14

In the inequality -2x + 3y ≤ 6, what is the slope of the boundary line?

-2/3
Explanation

Slope of boundary line: -2/3.

#15

When graphing the inequality y > 2x - 1, which direction should the shading be relative to the boundary line?

Above the line
Explanation

Shading above the line.

#16

Which of the following inequalities has no solution?

x > 2x - 1
Explanation

No solution: x > 2x - 1.

#17

In the inequality system 3x - 2y ≥ 6 and y < x + 2, how many points satisfy both inequalities?

2
Explanation

Two points satisfy both.

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