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Linear or Nonlinear? (Equations) — Easy Worksheet 1
Grade 8 · Whoobee Name: ____________________ Date: __________
Write "linear" or "nonlinear" for each equation.
How to solve
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Example
Is the function y = 9x + 8 linear or nonlinear?
Answer: linear
Not quite. The answer is
💡 y = 2x is y = 2x + 0. It has the form y = mx + b with m = 2 and b = 0, so its graph is a straight line. It is linear.
✓ Correct!
Not quite. The answer is
💡 y = 2x is y = 2x + 0. It has the form y = mx + b with m = 2 and b = 0, so its graph is a straight line. It is linear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = 5x linear or nonlinear?
✓ 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
💡 y = 2x + 6. It has the form y = mx + b with m = 2 and b = 6, so its graph is a straight line. It is linear.
✓ Correct!
Not quite. The answer is
💡 y = 2x + 6. It has the form y = mx + b with m = 2 and b = 6, so its graph is a straight line. It is linear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = 4x² linear or nonlinear?
✓ 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
💡 y = x² − 1 has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
✓ Correct!
Not quite. The answer is
💡 y = x² − 1 has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = 6x linear or nonlinear?
✓ 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
💡 y = x² + 9 has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
✓ Correct!
Not quite. The answer is
💡 y = x² + 9 has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = x² − 2 linear or nonlinear?
✓ 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
💡 y = 2x² has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
✓ Correct!
Not quite. The answer is
💡 y = 2x² has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = 2x + 3 linear or nonlinear?
✓ 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
💡 y = x² − 2 has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
✓ Correct!
Not quite. The answer is
💡 y = x² − 2 has an x² term, so it cannot be written as y = mx + b. Its graph is a curve, not a straight line, so it is nonlinear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = 7x linear or nonlinear?
✓ 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
💡 y = 9x is y = 9x + 0. It has the form y = mx + b with m = 9 and b = 0, so its graph is a straight line. It is linear.
✓ Correct!
Not quite. The answer is
💡 y = 9x is y = 9x + 0. It has the form y = mx + b with m = 9 and b = 0, so its graph is a straight line. It is linear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = x² − 4 linear or nonlinear?
✓ 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
💡 y = 5x is y = 5x + 0. It has the form y = mx + b with m = 5 and b = 0, so its graph is a straight line. It is linear.
✓ Correct!
Not quite. The answer is
💡 y = 5x is y = 5x + 0. It has the form y = mx + b with m = 5 and b = 0, so its graph is a straight line. It is linear.
💡 How to solve: Linear or Nonlinear? (Equations)
A function is linear when its equation can be written as y = mx + b (x to the first power only). Simplify first: multiply out brackets, collect like terms and get y on its own. If an x² or x³ term is left, or x is in a denominator, an exponent or under a square root, the function is nonlinear.
Try a similar one
Is the function y = x² − 7 linear or nonlinear?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Linear or Nonlinear? (Equations) — Easy Worksheet 1
Write "linear" or "nonlinear" for each equation.