Testinar Grade 8 math

Graphing Linear Inequalities in Two Variables

Learn to reason about and solve Grade 8 problems involving Graphing Linear Inequalities in Two Variables.

CH03-09 Equations, Inequalities, and Systems

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

The graph shows a solid line and shading above. The point \((3,5)\) is marked in the shaded region. Which inequality is represented?
1. \(y > x + 1\)
2. \(y \geq x + 1\)
3. \(y < x + 1\)
4. \(y \leq x + 1\)
Based on the dashed line and shaded region, what inequality is shown?
1. \(y > -x + 2\)
2. \(y < -x + 2\)
3. \(y \geq -x + 2\)
4. \(y \leq -x + 2\)
Graph \(y \geq \frac{1}{2}x\). Which region should be shaded?
1. Below the line only
2. Above the line only
3. Above and on the line
4. Below and on the line
The graph shows which inequality?
1. \(y > 2x\)
2. \(y < 2x\)
3. \(y \geq 2x\)
4. \(y \leq 2x\)
What inequality matches this graph?
1. \(y > -3x\)
2. \(y < -3x\)
3. \(y \geq -3x\)
4. \(y \leq -3x\)
Which inequality is represented?
1. \(y \geq 3\)
2. \(y \leq 3\)
3. \(y > 3\)
4. \(y < 3\)
The graph shows which inequality?
1. \(x < 1\)
2. \(x > 1\)
3. \(x \leq 1\)
4. \(x \geq 1\)
Which inequality matches the graph?
1. \(y > x + 1\)
2. \(y < x + 1\)
3. \(y \leq x + 1\)
4. \(y \geq x + 1\)

Teacher and parent reference

Answer key and explanations

B. \(y \geq x + 1\)
The solid line (boundary included) with shading ABOVE indicates \(y \geq x + 1\). Verify: \((3,5)\) gives \(5 \geq 3+1=4\) ✓ TRUE.
B. \(y < -x + 2\)
DASHED line means \(>\) or \(<\). Shading BELOW means \(y <\). Combined: \(y < -x + 2\).
C. Above and on the line
The inequality \(\geq\) means "greater than or equal," so shade ABOVE the line. The SOLID line is included in the solution.
D. \(y \leq 2x\)
SOLID line (includes boundary) and shading BELOW the line indicates \(y \leq 2x\).
A. \(y > -3x\)
The DASHED line and shading ABOVE indicate a strict inequality with \(y\) greater: \(y > -3x\).
A. \(y \geq 3\)
Solid horizontal line at \(y = 3\) with shading ABOVE means \(y \geq 3\).
A. \(x < 1\)
Dashed vertical line at \(x = 1\) with shading to the LEFT means \(x < 1\).
C. \(y \leq x + 1\)
SOLID line (includes boundary) and shading BELOW indicate \(y \leq x + 1\).