equations

Linear equations in two variables
A common form of a linear equation in the two variables x and y is


where m and b designate constants (the variable y is multiplied by the constant 1, which as usual is not explicitly written). The origin of the name "linear" comes from the fact that the set of solutions of such an equation forms a straight line in the plane. In this particular equation, the constant m determines the slope or gradient of that line; and the constant term b determines the point at which the line crosses the y-axis.

Since terms of a linear equations cannot contain products of distinct or equal variables, nor any power (other than 1) or other function of a variable, equations involving terms such as xy, x², y1/3, and sin(x) are nonlinear.