Line QR contains (2, 8) and (3, 10) Line ST contains points (0, 6) and (-2,2). Are lines QR and ST parallel or perpendicular?

Lines are parallel.

Explanation:

For finding whether lines #QR# and #ST# are parallel or perpendicular, what we need is ti find their slopes.

If slopes are equal , lines are parallel and if product of slopes is #-1#, they are perpendicular .

The slope of a line joining points #(x_1,y_1)# and #x_2,y_2)# is #(y_2-y_1)/(x_2-x_1)#.

Hence slope of #QR# is #(10-8)/(3-2)=2/1=2#

and slope of #ST# is #(2-6)/(-2-0)=(-4)/(-2)=2#

As the slopes are equal, lines are parallel.
graph{(y-2x-4)(y-2x-6)=0 [-9.66, 10.34, -0.64, 9.36]}