Using the Slope Formula

If you know the coordinates of two points on a line and the line is not horizontal or vertical, the slope can always be found by the following formula:

You should realize that is doesn't matter which two points you use to find the slope.  If they are on the same line, then any two slope-triangles on the line will give the same fraction for slope when it is reduced.  It also follows that parallel lines have the same slope.

If you do not know the y-intercept for a slanting line, the slope formula gives a simple method for finding the equation:  Use a "generic point" (x, y) in place of (x₂, y₂) and equate the slopes.  Then "simplify" by multiplying both sides by the denominator.

Example:  Find an equation of this line:

Solution:  Using the slope formula with (x, y) in place of (x₂, y₂) and (6, 5) in place of (x₁, y₁) we have:

   

 

 

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