📖Definition
A linear equation is an algebraic equation where each term is either a constant or the product of a constant and a single variable. When graphed, it forms a straight line. The name "linear" comes from the fact that these equations always create straight lines.
📐Formula
In this form: m represents the slope (steepness) of the line, b represents the y-intercept (where the line crosses the y-axis), and x and y are variables.
📝Step-by-Step Guide
Simplify both sides
Combine like terms and distribute any parentheses on each side of the equation.
Move variable terms to one side
Add or subtract to get all variable terms on one side of the equation.
Move constant terms to the other side
Add or subtract to get all constants on the opposite side from the variable.
Isolate the variable
Divide or multiply both sides to solve for the variable.
⚠️Common Mistakes to Avoid
- Forgetting to perform the same operation on both sides
- Sign errors when moving terms across the equals sign
- Not distributing multiplication over parentheses correctly
- Confusing slope and y-intercept in slope-intercept form
✏️Practice Problems
Solve 3x + 7 = 22
Answer: x = 5
Solve 2(x - 3) = 4x + 6
Answer: x = -6
Solve (2x + 1)/3 = (x - 2)/2
Answer: x = -8
Ready to Practice Linear Equations?
Generate a personalized practice test with MathQuizily. Get instant PDF downloads with answer keys.