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

1 Answer
Mar 13, 2018

Answer:

The point #(1,18)# is one possible point on the second line.

(but there is literally an infinite number of possible points)

Explanation:

The lines are parallel so they will have the same gradient (slope). First we find the gradient of the first line:

#m=(y_2-y_1)/(x_2-x_1)=(7-2)/(5-6)=5/(-1)=-5#

To find the y-intercept we can write the equation of the line in gradient-intercept form:

#y=mx+c#

We rearrange this equation and plug in the #x# and #y# values of the point we have:

#c=y-mx=8-(-5)(3)=8+15=23#

The equation of the second line, then, is #y=-5x+23#. Any set of #x# and #y# that makes that equation true is a point on the second line.

Let's use #x=1#, then #y=-5(x)+23=18#, so the point #(1,18)# is on the second line.