What is the connection between linear graphs and linear equations?
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one, two, three or more 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 set of solutions of such an equation forms a straight line in the plane, which is the origin of the name “linear”. 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.
