What Does Linear Mean in Mathematics?

Johnathan Nightingale/CC-BY-SA 2.0

In mathematics, linear refers to an equation or function that is the equation of a straight line and takes the form y = mx + b, where “m” is equal to the slope, and “b” is equal to the y-intercept. Three features define a function as linear, but if a function satisfies one of the three requirements, then it satisfies them all and can be classified as linear.

First, the function must be of order one. This means that the highest degree or exponent in the function must be one. In other words, if any variable is squared, cubed or raised to any power but one, the function is not linear. Next, the function must be the equation of a straight line. This can be verified most easily by graphing the function, but if the function satisfies the third quality, then it must also satisfy the second. The third requires that the function take the form y = mx + b. A function can take this form without appearing to do so. For example, y = 4 is linear; “m” is zero and “b” is four. If a function takes this form, then it is either increasing, decreasing or remaining constant at some fixed rate. A fixed rate means that points on the graph are evenly spaced, forming a straight line.