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Graphs of Linear Equations in Two Variables
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Forms of Linear Equations

Two-Point Form

The following is the two-point form of the equation of a line:

y− y 1 =( y 2 − y 1 x 2 − x 1 )(x− x 1 )

where ( x 1 ,   y 1 ) and ( x 2 ,   y 2 ) are two points on the line and x 1 ≠ x 2 .



Example

Write an equation of the line that passes through the points (1,  −6) and (9,  −2). Express your final answer in general form.



Solution

Using the two-point form with points ( x 1 ,   y 1 )=(1,  −6) and ( x 2 ,   y 2 )=(9,  −2), you will get:

y−(−6)=[ −2−(−6) 9−1 ](x−1)         y+6=( −2+6 8 )(x−1)         y+6= 1 2 (x−1)    2y+12=x−1.

Writing the last equation in general form, you will get:

x−2y−13=0.