Lines and the Coordinate Plane: Slope of a Line

Solving for an Unknown Coordinate

You can solve equations to determine an unknown coordinate.  This is useful if you have a starting point and know the rate of increase in a real-world situation.  Suppose that you know that the population of a town in 1984 was 34,000 and that the population grew by 500 people per year (the slope).  You could use the method below to determine a missing value, such as the population in 2000.

Example 1

Find the value of x so that the slope of the line passing through (x, 5) and (2, 8) is -1.
x is the missing coordinate.  Set up the equation as you just learned to do, then solve for x.

m equals y 2 minus y 1 divided by x 2 minus x 1, negative 1 equals 8 minus 5 divided by 2 minus x, corss multiply to get negative 1 times the quantity 2 minus x equals 8 minus 5, negative 2 plus x equals 3, x equals 5

So, 5 is the missing coordinate.

Example 2

Find the value of y so that the slope of the line passing through (2, 8) and (5, y) is one-half.

one-half equals y minus 8 divided by 5 minus 2, one-half equals y minus 8 divided by 3, cross multiply, 3 equals 2 times the quantity y minus 8, 3 equals 2 y minus 16, 19 equals 2 y, y equals nineteen-halves