Point-Slope Equation

The point-slope form .is used to determine the equation of a line given a point on the line and a slope.
Find the equation of a line through (4,1) whose slope is .

                 … substituting (4,1) for and

                             … solving for y

Find the equation of a line through (5,-7) perpendicular to .

In order to use the point-slope form, it is necessary to have a point and the slope.  Find the slope from the given line.  Solve the equation of the line for y to determine the slope.

                 … divide all terms by 2

 … the slope of this line is

To find an equation of a line perpendicular to this line … the slope of the perpendicular line would be .  Remember the point (5,-7) was given.

After finding the equation of the line in slope-intercept form you may be asked to change the equation back into the standard form of Ax + By = C.  Remember that the standard form is Ax + By = C, where A, B, and C are Integers and A > 0 (in other words A is positive.)

So to transform the above equation:
                                 
... First multiply all terms by LCD = 5
    
 

     ... Now move the x-term to the left-hand side of the equation (additive inverses)

         ... Finally multiply all terms by negative one so that "A" is positive

    

Now the equation is in the standard form.

 

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 09-Jan-2014