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Equation of a Line

How to Determine the Equation of a Line

This is a graph of a pair of linear equations or linear functions.

HiTe, public domain
There are many instances in science and math in which you will need to determine the equation of a line. In chemistry, you'll use linear equations in gas calculations, when analyzing rates of reaction, and when performing Beer's Law calculations. Here's a quick overview and example of how to determine the equation of a line from (x,y) data.

A linear equation or equation of a line has the following form:

y = mx + b

m: slope of the line; m = Δx/Δy

b: y-intercept, which is where the line cross the y-axis; b = yi - mxi

Example: Determine the equation of a line using the following (x,y) data.

(-2,-2), (-1,1), (0,4), (1,7), (2,10), (3,13)

First calculate the slope m, which is the change in y divided by the change in x:

y = Δy/Δx

y = [13 - (-2)]/[3 - (-2)]

y = 15/5

y = 3

Next calculate the y-intercept:

b = yi - mxi

b = (-2) - 3*(-2)

b = -2 + 6

b = 4

The equation of the line is

y = mx + b

v = 3x + 4

Anne Marie Helmenstine, Ph.D.

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