Graphing Inequalities Quiz

1. What type of boundary line should be drawn for the inequality $y \geq 2x - 5$?

• A. Dashed line
• B. Solid line
• C. No line is needed
• D. A dotted curve

2. Using the test point $(0,0)$, which region satisfies $y < 3x + 2$?

• A. The region above the line
• B. The region below the line
• C. The region on the line only
• D. The region to the right of the line

3. A feasible region is bounded by $x = 2$ and $y = 8 - x$. What is the vertex where these two lines meet?

• A. (2, 6)
• B. (6, 2)
• C. (2, 8)
• D. (8, 2)

4. A region satisfies $x \geq 0$, $y \geq 0$, and $x + y \leq 5$. Which of the following points lies in the feasible region?

• A. (-1, 2)
• B. (3, 3)
• C. (2, 2)
• D. (6, 0)

5. For the system $y \leq x + 4$, $y \geq -x + 2$, and $x \leq 3$, the feasible region is a triangle. To maximise $P = 2x + y$ over this region, what should you do?

• A. Evaluate $P$ at the centre of the triangle
• B. Evaluate $P$ at each vertex of the triangle and compare
• C. Evaluate $P$ only where $x = 3$
• D. Estimate $P$ using the area of the triangle