Section 1-3:  Finding Equations of Lines 
Linear equations can be written in many different ways.  The following chart represents a few of the more useful methods:
    The general form Ax + By = C Form used for answers.. 

A,B,C cannot be fractions

The slope-intercept form  y = mx + b Line has slope m and 

y-intercept b.

  The point-slope form y-y1 = m(x-x1) Line has slope m and 

contains (x1, y1)

   The intercept form   Line has x-intercept a and 

y-intercept b.

Sample problems
x/6 + y/3 = 1
multiply by 6 to eliminate the fractions
x + 2y = 6

m = (5 - (-1))/(1 - 5) = 6/-4 = -3/2
Now use the point- slope form using one of the given points.  It doesn't matter which one!
(y - 5) = (-3/2)(x - 1)
multiply by 2 to eliminate the fraction.
2y - 10 = -3x + 3
Put in general form
3x + 2y = 13  (Voila!)

4x + y = 2
y = -4x + 2
The slope m = -4
Now use the slope-intercept method to find the equation.
y = -4x - 2
4x + y = -2

This is the point that the perpendicular bisector goes through.  Now find the slope.
m = (-5 - 3)/(4 - (-2)) = -8/6 = -4/3
But the perpendicular slope is a negative reciprocal.  So,
m = 3/4
Now use the point-slope form and get:
y - (-1) = (3/4)(x - 1)
Multiply by 4 to eliminate the fraction.
4y + 4 = 3x - 3
Put in the general form:
-3x + 4y = -7 or 3x - 4y = 7 (why?)