What is a Linear Equation?
A linear equation is an equation where the variable appears only to the first power, producing a straight line when graphed. Solving one means finding the value of the variable that makes the equation true.
A linear equation in one variable has the form ax + b = 0, and its solution is x = −b/a (for a ≠ 0). It represents a straight line when the equation involves two variables.
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Step-by-step worked examples
Solve 2x − 6 = 0.
Add 6 to both sides: 2x = 6 Divide both sides by 2: x = 3
Solve 3x + 9 = 0.
Subtract 9 from both sides: 3x = −9 Divide both sides by 3: x = −3
Solve −4x + 20 = 0.
Subtract 20 from both sides: −4x = −20 Divide both sides by −4: x = 5
Flashcards
Quick quiz
Q1.Solve 5x − 15 = 0.
Q2.What is the solution formula for ax + b = 0?
Q3.A linear equation's graph is always a…
Q4.Solve x/4 + 2 = 0.
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Common mistakes
Forgetting to flip the sign when moving a term across the equals sign. — Correct: Moving b to the other side changes its sign: ax = −b, not ax = b.
Dividing by a without checking a ≠ 0. — Correct: If a = 0, the equation isn't linear in x anymore — check first before dividing.
Mixing up the coefficient a and the constant b. — Correct: a always multiplies x; b stands alone — keep them separate when isolating x.
Stopping after isolating ax instead of dividing by a. — Correct: The final step must isolate x completely: divide both sides by a.
FAQ
What is the formula for a linear equation?
The standard one-variable form is ax + b = 0, solved as x = −b/a.
What is a linear equation, in simple terms?
An equation where the unknown appears only to the first power, so its graph is a straight line.
How to solve a linear equation step by step?
Isolate the variable term, then divide by its coefficient: ax = −b, so x = −b/a.
What are examples of linear equations?
2x − 6 = 0, 3x + 9 = 0, and y = 2x + 1 are all linear equations.