What is a linear pattern?

A linear pattern exists if the points that make it up form a straight line. In mathematics, a linear pattern has the same difference between terms. The patterns replicate on either side of a straight line.

An example is a line of the form y = mx + c, with (x, y) coordinates (1, 5), (2, 7) and (3, 9). In the example, the difference between the x coordinates of any two consecutive terms is 1, as given by 2 - 1 or 3 - 2. Similarly, the difference in the y coordinates is 2 (7 - 2 or 9 - 7). Based on observation, it’s possible to predict any other possible coordinates of the linear pattern. For example, the next coordinates after (3, 9) are (3 + 1, 9 + 2) or (4, 11). It’s also possible to identify a mathematical relationship between the x and y coordinates of a linear equation with points (1, 2), (2, 4) and (3, 6). If x = 1, y =2 and x =2, y = 4, then y is twice x, which is represented algebraically as y = 2x.

Similar patterns are spotted in weaving, beading paper and music that has a linear beat. Stripes on clothing, footprints and zippers show linear patterns as well. The passage of the day and seasonal changes exhibit repetition that’s consistent with linearity.