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How to Write Equations for Linear Growth Patterns

Even students who understand linear equations in algebra problems sometimes find them difficult to identify and work with when they appear in the context of a real-world graph. One of the most common types of graph is that of growth patterns. These graphs show the relationship between time on the x-axis and measurement of amount on the y-axis. In terms of the coordinate plane, they represent only the first quadrant because neither time nor amount will have a negative value.

Instructions

- 1
  Locate two easy-to-identify points on the graph. Write them down as coordinate pairs with time as the x and amount as the y. For instance, if the line passes through a point that lines up vertically with 10 years and horizontally with a height of 43 feet, you would write down (10,43).
- 2
  Use the formula (y2-y1)/(x2-x1) to find the slope, or rate of growth. Plug in the y coordinates from each point as y2 and y1 and the x coordinates from each point as x2 and x1. For instance, if the points were (10,43) and (15,68), you would do (68-43)/(10-5) to get 15/5 which reduces to 3. Write this number down.
- 3
  Find the starting point of the graph on the y-axis and write it down. For example, if the initial height is 8 inches, you would record 8.
- 4
  Write the equation of the growth pattern by using the slope-intercept form of a line: y=mx+b. Put in the number from Step 2 for m and the number from Step 3 for b. Here, you would end up with y = 3x + 8.

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