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A line passes through #(4 ,3 )# and #(7 ,1 )#. A second line passes through #(1 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

The two lines have the same slope because they are parallel.

One point on the second line is #(3/2,2)#.

In order to solve this question, we need to find the slope of the first line. The second will have the same slope, since they are parallel.

#m=(y_2-y_1)/(x_2-x_1)# #=(1-3)/(7-4)=-2/3#

If we write the equation of the second line as:

#y=mx+c# we can substitute in the value of #m#:

#y=2/3x+c#

We can substitute in the point #(1,1)# to find the value of #c#:

#1=2/3(1)+c#

#c=1/3#

So #y=2/3x+1/3#

Any point that we can substitute into this equation that makes it true is a point on that line. Let's choose #y=2# and find the value of #x# that makes the equation too:

#2=2/3x+1/3#

#x=3/2#

One point on the second line, then, is #(3/2,2)#.

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