A line passes through (-7,1) and (-2,6).
Another lines passes through (-5,-1) and (0,4).
Prove the points are parallel. If the gradients of the two lines are the same , then the lines are parallel.
Line 1
( x 1 , y 1 ) = (-7,1) and ( x 2 , y 2 ) = (-2,6).
m = ( y2 - y1 ) / ( x2 - x 1 )
m = ( 6 - 1 ) / ( -2 - - 7 ) = 5 / 5 = 1
Line 2
( x 1, y 1 ) = ( -5 , -1 ) and ( x 2 , y2 ) = ( 0 , 4 )
m = ( 4 - - 1 ) / 0 - - 5 ) = 5 / 5 = 1
The slope of Line 1 is 1 ( CORRECT )
The slope of Line 2 is 1 ( CORRECT )
Both lines have the same slope so they are parallel ( CORRECT)