3 The equation of a straight line through two points

The equation of the line passing through the points with coordinates A ( x 1 , y 1 ) and B ( x 2 , y 2 ) is given by the following formula.

Key Point 9

The line passing through points A ( x 1 , y 1 ) and B ( x 2 , y 2 ) is given by

y y 1 y 2 y 1 = x x 1 x 2 x 1 or, equivalently y y 1 = y 2 y 1 x 2 x 1 ( x x 1 )

Task!

Find the equation of the line passing through A ( 7 , 11 ) and B ( 1 , 3 ) .

First apply the formula: y y 1 y 2 y 1 = x x 1 x 2 x 1

y 11 3 11 = x + 7 1 + 7 .

Simplify this to obtain the required equation:

y = 4 x

Exercises
  1. Find the equation of the line joining ( 1 , 5 ) and ( 9 , 2 ) .
  2. Find the gradient and vertical intercept of the line joining ( 8 , 1 ) and ( 2 , 3 ) .
  1. y = 3 10 x + 47 10 .
  2. 0.4, 2.2 .