How to Calculate Linear Growth With Algebra

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When an object, organism or group of organisms grows, it increases in size. Linear growth refers to a change in size that proceeds at the same rate over time. Linear growth on a graph looks like a line that slopes upward as it proceeds to the right. Calculate linear growth by figuring out the slope of the line.

The Slope of a Linear Growth Line

A line graph has an x-axis and a y-axis. The y-axis is the vertical axis labeled with the variable being measured. The x-axis is the horizontal axis labeled with the variable that influences the variable being measured. When you plot any data point, you create an x,y coordinate. The slope of a line, and therefore linear growth, is calculated using two coordinates: (x1, y1) and (x2, y2). The formula for calculating slope is:

slope = (y2 - y1) / (x2 - x1)

Calculating Linear Growth

Imagine a graph that shows the growth in height of a flower over 10 days. If the graph shows an upwardly sloping line, the flower is experiencing linear growth. Calculate the linear growth of the flower the same way you would calculate the slope of the line. Suppose two sets of x and y coordinates on the graph are (2, 5) and (7, 10). This would mean that on day two the flower was 5 centimeters tall and on day seven the flower was 10 centimeters tall. Calculate the rate of linear growth by dividing the difference in height by the difference in time, as follows:

(10 cm - 5 cm) / (7 days - 2 days) = 5 cm / 5 days

This answer means that the flower grew 5 centimeters in five days. Simplifying 5/5 gives you 1, meaning the flower experienced a linear growth rate of 1 centimeter per day.

References

About the Author

Tim Banas started writing professionally in 2009 after teaching high school science for seven years. He has since written and edited for various online publications including Demand Studios, FYILiving.com, Tree.com and BinaryOption.com. He has a Master of Science in biology from Southern Illinois University.

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  • Thomas Northcut/Digital Vision/Getty Images

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