A linear equation has variables raised only to the first power. No squares, no cubes, no roots. The standard form is Ax + By = C, and the slope-intercept form is y = mx + b. The graph is always a straight line.

Solving a linear equation means finding the value that makes it true. For 3x + 5 = 14, subtract 5 from both sides, then divide by 3: x = 3. Systems of linear equations can be solved by substitution, elimination, or matrices.

Linear equations model constant rates. Distance at constant speed, cost at a fixed price per unit, and simple interest are all linear. They are the simplest equations to solve and the first type students master. Their simplicity makes them powerful in applications where relationships are proportional.

• Variables to the first power only
• Graph is a straight line
• Forms: Ax + By = C, y = mx + b
• Models constant rates and proportional relationships