Know these formulas:

Slope:       
( x₁ ¹ x₂   because this would cause the
fraction to be undefined)

Point-Slope:      y – y₁ = m ( x – x₁ )
(x₁, y₁) = coordinates of given point

   To find the equation of a (non-vertical or non-horizontal) line you must know the slope and one point

  1.  If the slope is not given, you must find it:

      a.  if you are given two points use the slope formula

         b.  if you are given an equation write in y = mx + b form so that you can see the slope m

  2.  Use the Point-Slope formula, replacing x₁ and y₁ with the coordinates of the point and m
         with the slope found in step 1.
  3.  Solve this equation for y.  This gives you the equation of the line in point-slope form:  y = mx + b. 

   4.  If you are asked to also write the equation in Ax + By = C form:

       a.  Clear the fractions from the equation.

       b.  Rewrite the equation so that both variables are on the left and the constant is on the right. 
            Be sure that the leading coefficient is positive.

Parallel Lines:           Same process as above using the same slope as the one in the given line. 

Perpendicular Lines:  Same process as above but use the
opposite sign and the reciprocal of the slope in the given line. 

Vertical Lines:   The equation is   x = the x-coordinate of the given point. 

Horizontal Lines:  The equation is   y = the y-coordinate of the given point.

Write the Equation of a Line When Given Two Points  (Alternate Method)

Write the equation of the line that passes through the points
(x₁, y₁) and (x₂, y₂)

Solve each equation for b
(The value for b should be the same in both equations)

Now write the equation in slope intercept form
using the slope and b you found:
y=mx+b
This is the equation of the line passing through the two given points.