By Tim Banas, Updated Aug 30, 2022
Thomas Northcut/Digital Vision/Getty Images
Linear growth describes a constant rate of change over time. In graph form, it manifests as a straight line that ascends steadily. Understanding how to calculate this growth using algebra is essential for fields ranging from biology to engineering.
A line graph consists of an x‑axis (time or another independent variable) and a y‑axis (the measured variable). Each plotted point yields an (x, y) coordinate. The slope, which represents the growth rate, is calculated from any two distinct points:
m = (y₂ – y₁) / (x₂ – x₁)
Consider a chart tracking a flower’s height over ten days. Suppose you pick the points (2, 5) and (7, 10), where the first number is days and the second is centimeters.
Using the slope formula:
m = (10 cm – 5 cm) / (7 days – 2 days) = 5 cm / 5 days = 1 cm/day
Thus, the flower exhibits a linear growth rate of one centimeter per day.
