How to Find an Equation Given a Table of Numbers

By Rebekah Richards

Sets of points on a line are sometimes expressed in tables of x- and y-values. If you have a table of values for a linear equation, you can plot these ordered pairs to get an approximate sense of the line, including an estimate of its slope and intercepts. If you need more precise measurements, you can figure out the equation from a table of values by calculating the slope of the line and then using the point-slope formula.

Calculate the slope of the line by selecting any two points in your table. Subtract the second y-value from the first y-value. Then subtract the second x-value from the first x-value. Divide the difference in the y-values by the difference in the x-values to find the slope. For example, if your first point is (5,4) and your second point is (8,10), (10-4)/(8-5) simplifies to 6/3, which equals a slope of 2.

Substitute the slope and one ordered pair into the point-slope equation: y - y1 = m(x - x1). In the equation, m represents the slope. For example, using the slope 2 and the ordered pair (8,10), the equation is y - 10 = 2(x - 8). This simplifies to y = 2x - 6.

Check your work by putting one value from an ordered pair in your table into your final equation and solving. For example, if you put (5,4) into y = 2x - 6, you get 4 = 2(5) - 6, which is correct.

About the Author

Rebekah Richards is a professional writer with work published in the "Atlanta Journal-Constitution," "Brandeis University Law Journal" and online at tolerance.org. She graduated magna cum laude from Brandeis University with bachelor's degrees in creative writing, English/American literature and international studies. Richards earned a master's degree at Carnegie Mellon University.