A line passes through (9 ,5 ) and (6 ,8 ). A second line passes through (7 ,3 ). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Mar 31, 2016

(color(green)(0,10))

Explanation:

A line passing through (9,5) and (6,8) has a slope of
color(white)("XXX")m=(Delta y)/(Delta x) = (8-5)/(6-9)=3/(-3) =-1

All parallel lines have the same slope.

So a parallel line passing through (7,3) and some other point (x,y) will have the form:
color(white)("XXX")(y-3)/(x-7)=-1
or
color(white)("XXX")y=10-x

Picking an arbitrary value for x, say x=0
we have
color(white)("XXX")y=10 as a corresponding point.

So one point that satisfies the given requirements is (0,10)