linear equation

Imagine a perfectly straight road on a map: no curves, no loops, just a steady line. A linear equation is the algebra behind that straightness. Every variable in it appears only to the first power — no x^2, no sqrt(x), no 1/x — so when you graph it you always get a straight line.

More precisely, a linear equation in one variable can always be rearranged into the form ax + b = 0, where a and b are numbers and a is not zero. In two variables it looks like ax + by = c. The defining feature is that variables are never multiplied together, never raised to a power other than one, and never buried inside roots or denominators.

Linear equations are the friendliest equations to solve: a single one in one unknown has exactly one solution (unless it secretly reduces to something always-true or always-false). That predictability is why they appear everywhere, from balancing a budget to converting temperatures.