Equations of Lines

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If you are given two points on the coordinate plane, there is only one straight line that passes through both of them. But what is the equation for that line? To find out, we follow a simple process: find the slope, find the y-intercept, and then put these values into the slope-intercept equation form. 

Let’s take a look at a simple example. We are given two points: (2, 4) and (6, 16). What is the equation for this line? We start by finding the slope. [Remember, the GED Math formula sheet will include both the formulas for slope and the slope-intercept form, so there’s no need to memorize them.]

We find slope like this:

  • Slope = (y₂ − y₁)/(x₂ − x₁)
  • Slope = (16 − 4)/(6 − 2)
  • Slope = 12/4
  • Slope = 3

The slope of our line is 3. Next, we take this value along with the x- and y-coordinates of one of the points, and solve the slope-intercept equation for the y-intercept. It does not matter which of the given points you use, the answer will be the same. Here, we will use (2, 4). Also, remember that in slope-intercept form, b is the y-intercept (the point where the line intersects the y-axis).

  • y = mx + b
  • 4 = (3)(2) + b 
  • 4 = 6 + b 
  • 4 − 6 = 6 − 6 + b
  • -2 = b

The y-intercept of our line is -2. We are now ready to write the equation of the line. Again, we are going to use slope-intercept form, substituting our values for the slope and y-intercept: y = 3x − 2. [Since the y-intercept is a negative, we subtract it in this version of the equation.] Finding the equation of a line when given two points is an essential skill for the algebra questions of the GED Math test. Here is a short quiz so you can practice what you’ve learned. Good luck!