A line passes through #(4 ,3 )# and #(1 ,4 )#. A second line passes through #(5 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Apr 9, 2016

One possible point: #(23,0)#

Explanation:

A line passing through #(4,3)# and #(1,4)#
has a slope of #(Delta y)/(Delta x)= (4-3)/(1-4)= -1/3#

If a line passing through #(5,6)# is parallel, it must have the same slope.

Therefore for any point #(x,y)# on this second line:
#color(white)("XXX")(y-6)/(x-5)= -1/3#
or
#color(white)("XXX")3y-18 = 5-x#
or
#color(white)("XXX")x+3y = 23#

For an easy to determine point, let #y=0#
#rarr x=23#

So another point on this second line would be #(23,0)#

graph{((x-4)^2+(y-3)^2-0.02)((x-1)^2+(y-4)^2-0.02)((x-5)^2+(y-6)^2-0.02)(x+3y-13)(x+3y-23)=0 [-5.25, 14.75, -0.626, 9.37]}