A linear equation is an equation whose graph forms a straight line, typically in the form ax + b = 0 or y = mx + b.
A linear equation in one variable (x) has the form ax + b = 0 with solution x = -b/a. In two variables, y = mx + b represents a line with slope m and y-intercept b. The standard form is Ax + By = C. Systems of linear equations can be solved by substitution, elimination, or matrix methods. Linear equations model proportional relationships and are the foundation of linear algebra.
Linear equations were solved by ancient Egyptians and Babylonians. The slope-intercept form y = mx + b was popularized by RenΓ© Descartes in the 17th century. The study of systems of linear equations led to the development of matrix algebra in the 19th century. Linear equations remain essential in every field of science and engineering.