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?

Question

1536 views around the world

You can reuse this answer
Creative Commons License

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.