A linear equation describes a straight-line relationship — each step in x changes y by a constant amount. The most useful form is slope-intercept form.
In y = 2x + 3, the slope is 2 (y rises 2 for every 1 that x increases) and the line crosses the y-axis at 3. A positive slope rises left-to-right; negative falls; zero is horizontal.
Solving for a variable
Isolate the unknown by undoing operations in reverse. To solve 2x + 3 = 11: subtract 3 (2x = 8), then divide by 2 (x = 4). Whatever you do to one side, do to the other.
Graphing
Plot the intercept (0, b), then use the slope as rise-over-run to find a second point and draw the line through them.
Frequently asked questions
What is slope-intercept form? y = mx + b, with m the slope and b the y-intercept.
What does slope tell me? How much y changes per unit change in x.
How do I solve for x? Undo operations step by step to isolate x.
Linear equations model any constant-rate situation — a flat fee plus a per-unit charge, distance at steady speed, and countless others. Spotting the slope (the rate) and the intercept (the starting value) in a word problem is often the whole battle.