A line passes through #(9 ,2 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Oct 5, 2016

#color(green)(""(20,0))#

Explanation:

The slope of the first line through #(9,2)# and #(3,5)# is
#color(white)("XXX")color(green)(m)=(Deltay)/(Deltax)=(5-2)/(3-9) = color(green)(-1/2)#

A second line through #(4,8)# parallel to the first line must also have a slope of
#color(white)("XXX")color(green)(m)=color(green)(-1/2)#
That is
#color(white)("XXX")color(green)(m)=(bary-8)/(barx-4)=color(green)(-1/2)#
for all points #(barx,bary)# on the second line.
#rarrcolor(white)("XXX")2bary-16=4-barx#

#rarrcolor(white)("XXX")barx= 20-2bary#

To find a point on the second line pick an arbitrary value for #bary# and solve for #barx#
For example, if #bary=0#
#color(white)("XXX")barx=20-2 * 0 = 20#
giving us the point #(20,0)# on the second line.