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Direct & Inverse Variation — Easy Worksheet 2
Grade 9 · MathSheets Name: ____________________ Date: __________
Solve each problem.
How to solve
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Example
If y varies directly with x, and y = 4 when x = 2, find y when x = 4.
Answer: 8
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 10 ÷ 5 = 2, so y = 2x. When x = 2: y = 2 × 2 = 4. The answer is 4.
✓ Correct!
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 10 ÷ 5 = 2, so y = 2x. When x = 2: y = 2 × 2 = 4. The answer is 4.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 15 when x = 5, find y when x = 2.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 4 × 6 = 24, so y = 24x. When x = 2: y = 24 ÷ 2 = 12. The answer is 12.
✓ Correct!
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 4 × 6 = 24, so y = 24x. When x = 2: y = 24 ÷ 2 = 12. The answer is 12.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 4 when x = 1, find y when x = 5.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 6 ÷ 2 = 3, so y = 3x. When x = 3: y = 3 × 3 = 9. The answer is 9.
✓ Correct!
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 6 ÷ 2 = 3, so y = 3x. When x = 3: y = 3 × 3 = 9. The answer is 9.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 16 when x = 4, find y when x = 3.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 2 × 9 = 18, so y = 18x. When x = 3: y = 18 ÷ 3 = 6. The answer is 6.
✓ Correct!
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 2 × 9 = 18, so y = 18x. When x = 3: y = 18 ÷ 3 = 6. The answer is 6.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 20 when x = 4, find y when x = 5.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 6 ÷ 2 = 3, so y = 3x. When x = 5: y = 3 × 5 = 15. The answer is 15.
✓ Correct!
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 6 ÷ 2 = 3, so y = 3x. When x = 5: y = 3 × 5 = 15. The answer is 15.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 3 when x = 1, find y when x = 5.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 3 × 15 = 45, so y = 45x. When x = 5: y = 45 ÷ 5 = 9. The answer is 9.
✓ Correct!
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 3 × 15 = 45, so y = 45x. When x = 5: y = 45 ÷ 5 = 9. The answer is 9.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 10 when x = 2, find y when x = 3.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 4 ÷ 2 = 2, so y = 2x. When x = 1: y = 2 × 1 = 2. The answer is 2.
✓ Correct!
Not quite. The answer is
💡 Direct variation means y = kx. Find k: k = y ÷ x = 4 ÷ 2 = 2, so y = 2x. When x = 1: y = 2 × 1 = 2. The answer is 2.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 10 when x = 2, find y when x = 3.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 5 × 12 = 60, so y = 60x. When x = 3: y = 60 ÷ 3 = 20. The answer is 20.
✓ Correct!
Not quite. The answer is
💡 Inverse variation means xy = k, so y = kx. Find k: k = x × y = 5 × 12 = 60, so y = 60x. When x = 3: y = 60 ÷ 3 = 20. The answer is 20.
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
Try a similar one
If y varies directly with x, and y = 3 when x = 1, find y when x = 4.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Direct & Inverse Variation — Easy Worksheet 2
Solve each problem.