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 are a quick overview and example of how to determine the equation of a line from (x,y) data.

There are different forms of the equation of a line, including the standard form, point-slope form, and slope-line intercept form.

If you are asked to find the equation of a line and are not told which form to use, the point-slope or slope-intercept forms are both acceptable options.

### Standard Form of the Equation of a Line

One of the most common ways to write the equation of a line is:

**Ax + By = C**

where A, B, and C are real numbers

### Slope-Intercept Form of the Equation of a Line

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

The y-intercept is written as the point *(0,b)*.

### Determine the Equation of a Line - Slope-Intercept 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

y = 3x + 4

### Point-Slope Form of the Equation of a Line

In the point-slope form, the equation of a line has slope m and passes through the point (x_{1}, y_{1}). The equation is given using:

**y - y _{1} = m(x - x_{1})**

where m is the slope of the line and (x_{1}, y_{1}) is the given point

### Determine the Equation of a Line - Point-Slope Example

Find the equation of a line passing through points (-3, 5) and (2, 8).

First determine the slope of the line. Use the formula:

m = (y_{2} - y_{1}) / (x_{2} - x_{1})

m = (8 - 5) / (2 - (-3))

m = (8 - 5) / (2 + 3)

m = 3/5

Next use the point-slope formula. Do this by choosing one of the points, (x_{1}, y_{1}) and putting this point and the slope into the formula.

y - y_{1} = m (x - x_{1})

y - 5 = 3/5 (x - (-3))

y - 5 = 3/5 (x + 3)

y - 5 = (3/5)(x + 3)

Now you have the equation in point-slope form. You could proceed to write the equation in slope-intercept form if you wish to see the y-intercept.

y - 5 = (3/5)(x + 3)

y - 5 = (3/5)x + 9/5

y = (3/5)x + 9/5 + 5

y = (3/5)x + 9/5 + 25/5

y = (3/5)x +34/5

Find the y-intercept by setting x=0 in the equation of the line. The y-intercept is at the point (0, 34/5).

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