How to Do Linear Growth
Linear growth is growth that occurs at the same rate over time. A town's population and a child's height could have linear growth. Linear growth equations and graphs are the same as linear equations. Linear equations form lines. The features that distinguish each line are the y-intercept and the slope. These features make up the equation for the linear growth. You can graph linear growth and determine the equation if you know enough information.
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Instructions
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Determine the units used to measure the time. For example, if a child grew 3 inches in 2 years and the growth was linear, the time is measured in years.
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Determine the unit used to measure the growth. In the example, the unit used to measure the growth is inches.
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Set up a graph with the time interval on the x-axis and the growth on the y-axis.
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Plot any known points. In the example, since there is no known starting height, use the origin, or the point (0, 0) and then plot a point at (2, 3) to represent that the child grew 3 inches over a period of 2 years.
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Connect the known points with a line. This line represents the linear growth.
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Determine the equation of the line if needed. To do this, locate the y-intercept, or where the line crosses the y-axis, and the slope using the equation m = (y2-y1)/(x2-x1). In the slope equation, you will need to determine two points on the line (x1, y1) and (x2, y2). These can be any two points. The y-intercept is in the form (0, b). Then plug these into the slope-intercept form y=mx+b. In the example, the y-intercept it (0, 0) and the slope is (3-0)/(2-0) = 3/2. The slope intercept form of the equation is y = 3/2x + 0 or y = 3/2x.
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