A line passes through #(2 ,4 )# and #(7 ,3 )#. A second line passes through #(8 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Burglar
Jun 1, 2016

It is #y=-1/5x+33/5#.

Explanation:

We start calculating the slope of the line passing by the first two points.

The generic question is
#y=mx+q#
substituting the points we have
#4=2m+q#
#3=7m+q#
From the first equation I have
#q=4-2m#
I substitute this value in the second equation
#3=7m+4-2m# then
#-1=5m# and
#m=-1/5#.

Now we know that all the lines with the same slope are parallels.
So the line passing by the third point has equation

#y=-1/5m+q# and we have to find the #q# imposing the passage from #(8,5)#.

#5=-1/5*8+q#

#q=5+8/5=33/5#

Then the equation of the desired line is

#y=-1/5x+33/5#.

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