How to Find an Equation Given a Table of Numbers

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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.

Tips & Warnings

  • As long as you have two ordered pairs, you can find the slope and the equation.
  • This strategy does not work for nonlinear equations, such as exponential equations, because they do not have a constant slope.

References

  • "Algebra"; Michael Buckley; 2006
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