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18 The Equation of a Line
In this chapter, you determine the equation of a line. The basic graph of all
of mathematics is the straight line. It is the simplest to draw, and it has the
unique property that it is completely determined by just two distinct points.
Because of this unique property, it is a simple matter to write the equation
of a line given just two items of critical information.
There are three common methods for determining the equation of a line.
Determining the Equation of a Line Given the Slope and y-Intercept
This is the simplest of the methods for determining the equation of a line. You
merely use the slope-y-intercept form of the equation of a line: ym=mxbx.
Problem Given the slope m = 3 and the y-intercept y = 5, write the
equation of the line.
Solution
Step 1. Recalling that the slope-y-intercept form of the equation of a line is
ymmmmmxbx , write the equation.
The equation of the line is y = 3 x + 5. (You can see why this is the
simplest method!)
