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.