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Media4Math  Finding the Equation of a Line Given Two Points

Line From Two Points Example 1

In this example, a linear function is derived based on two points in Quadrant I, resulting in the equation of a line with positive slope.

Review of finding the equation of a line given two points:

Recall that if you know the slope and y-intercept of a line, you can write the equation of a line in slope-intercept form.

slope-intercept form

On the other hand, if all you know is the slope of the line and the coordinates of a point on the line, then you can write the equation of a line using the point-slope form. In this equation, m is the slope of the line.

point-slope form

In the case where all you know is the coordinates of two points but no other information, then neither the slope-intercept form nor the point-slope form can be used directly to write the equation of the line. Instead, a two-step process is required to find the equation:

  1. Use the coordinates of the two points to find the slope of the line connecting the two ponts. Do this using the slope formula. This will give you the value of slope m.
  2. Use the slope and one of the points to find the equation of the line using the point-slope form.

This two-step process will result in the equation of the line connecting the two points, written in slope-intercept form.

In this set of Math Tutorials, we show how to find the equation of a line given two points. We go through the two steps—calculating the slope m, finding the equation using the point-slope form. We look at different combinations of points relative to the four quadrants of the Cartesian coordinate plane. We look at equations with positive slope and equations with negative slope. The most straightforward examples are when both points are in Quadrant I, but we look at all combinations of point locations, taking into account various combinations of signed numbers.

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