A line passes through #(5 ,6 )# and #(7 ,3 )#. A second line passes through #(2 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2018-05-16T21:34:43

#color(blue)((1,19/2)#

First we need to find the equation of the line that passes through the points #(5,6) and (7,3)#

Using point slope form of a line:

#(y_2-y_1)=m(x_2-x_1)#

Where #m# is the gradient.

#m=(y_2-y_1)/(x_2-x_1)=(6-3)/(5-7)=-3/2#

#y-3=-3/2(x-7)#

#y=-3/2x+27/2#

The line passing through point #(2,8)# has to be parallel to the line we just found. If two lines are parallel, then they have the same gradients.

Using point slope form of a line:

#y-8=-3/2(x-2)#

#y=-3/2x+11#

To find another point that this line passes through, we just plug in a value for #x# and calculate the corresponding value of #y#

#x=1#

#y=-3/2(1)+11=19/2#

So #(1,19/2)# in another point.