FREE Download Printable Graphing Linear Inequalities Worksheets [PDFs] - Free Printable

Let’s solve each linear inequality step by step. We’ll rewrite each one in slope-intercept form (y = mx + b) so we can graph it easily. Remember:

- If you multiply or divide by a negative number, flip the inequality sign.
- Graph the line as dashed if the inequality is < or >, solid if ≤ or ≥.
- Shade above the line for y > or y ≥, below for y < or y ≤.

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1) -2x - 7 < -3y

Step 1: Solve for y
Add 3y to both sides:
-2x - 7 + 3y < 0
→ 3y < 2x + 7

Divide by 3:
y < (2/3)x + 7/3

Graph: Dashed line with slope 2/3, y-intercept 7/3 ≈ 2.33. Shade BELOW.

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2) -⅔x - 1 < -y

Step 1: Multiply both sides by -1 → FLIP inequality:
(2/3)x + 1 > y
→ y < (2/3)x + 1

Graph: Dashed line, slope 2/3, y-intercept 1. Shade BELOW.

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3) -7x + 5y ≤ -6

Step 1: Add 7x to both sides:
5y ≤ 7x - 6

Divide by 5:
y ≤ (7/5)x - 6/5

Graph: Solid line, slope 7/5 = 1.4, y-intercept -1.2. Shade BELOW.

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4) x - 2y ≤ 4

Step 1: Subtract x:
-2y ≤ -x + 4

Divide by -2 → FLIP inequality:
y ≥ (1/2)x - 2

Graph: Solid line, slope 1/2, y-intercept -2. Shade ABOVE.

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5) -2y > -3x - 6

Step 1: Divide by -2 → FLIP inequality:
y < (3/2)x + 3

Graph: Dashed line, slope 3/2 = 1.5, y-intercept 3. Shade BELOW.

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6) 5 < -y

Step 1: Multiply by -1 → FLIP inequality:
-5 > y → y < -5

Graph: Horizontal dashed line at y = -5. Shade BELOW.

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7) -4x + 12 > -3y

Step 1: Add 3y to both sides:
-4x + 12 + 3y > 0
→ 3y > 4x - 12

Divide by 3:
y > (4/3)x - 4

Graph: Dashed line, slope 4/3 ≈ 1.33, y-intercept -4. Shade ABOVE.

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8) -8 + 4y ≥ -3x

Step 1: Add 8 to both sides:
4y ≥ -3x + 8

Divide by 4:
y ≥ (-3/4)x + 2

Graph: Solid line, slope -3/4, y-intercept 2. Shade ABOVE.

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9) y - ⅙x > -1

Step 1: Add ⅙x to both sides:
y > (1/6)x - 1

Graph: Dashed line, slope 1/6, y-intercept -1. Shade ABOVE.

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Final Answer:
Here are the rewritten inequalities ready for graphing:

1) y < (2/3)x + 7/3
2) y < (2/3)x + 1
3) y ≤ (7/5)x - 6/5
4) y ≥ (1/2)x - 2
5) y < (3/2)x + 3
6) y < -5
7) y > (4/3)x - 4
8) y ≥ (-3/4)x + 2
9) y > (1/6)x - 1

For each, draw the line (dashed for < or >, solid for ≤ or ≥), then shade the correct side based on the inequality direction.