Question

A line passes through . If slope of the line is m , show that .

Answer 1

The given points are ( x 1 , y 1 ) and ( h,k ) through which the line passes. It is also given that the slope of the line is m.

The formula for the slope of a line passing through two different points ( x 2 , y 2 ) and ( x 3 , y 3 )is given by,

m= y 3 − y 2 x 3 − x 2 (1)

Substitute the values ( x 1 , y 1 ) and ( h,k ) for ( x 2 , y 2 ) and ( x 3 , y 3 ) in equation (1).

m= k− y 1 h− x 1 ( k− y 1 )=m⋅( h− x 1 )

Hence, ( k− y 1 )=m⋅( h− x 1 ).