A linear equation is an equation that forms a straight line when graphed. The most common form is slope-intercept: y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept (where the line crosses the y-axis).
To solve a linear equation, isolate the variable by performing inverse operations on both sides. For example, to solve 3x + 7 = 22, subtract 7 from both sides to get 3x = 15, then divide by 3 to get x = 5.
The slope m can be calculated from two points (x₁, y₁) and (x₂, y₂) using the formula: m = (y₂ - y₁) / (x₂ - x₁). A positive slope means the line rises from left to right; a negative slope means it falls.
Linear equations model many real-world situations: distance over time at constant speed, cost with a fixed fee plus per-unit pricing, and temperature conversions between scales.