A line passes through #(5 ,6 )# and #(2 ,8 )#. A second line passes through #(7 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
bp
Jan 8, 2017

One specific point would be (4,3)

Explanation:

Slope of the line passing through (5,6) and (2,8) would be #(8-6)/(2-5)= -2/3#

Slope of the line parallel to this one would also be #-2/3#. If the line passing through (7,1) also passes through a point #(x, y)#, then its slope can also be expressed as #(y -1)/(x -7)#

Then #-2/3 = (y -1)/(x -7)#. Solve this eq. for y.

#y= (17-2x)/3#. Now assign any value to x and calculate the corresponding y. Thus there would be infinite number of points
satisfying the equation.

A specific point can be obtained by assigning the value x=4 for which y would be 3. this point would thus be (4,3).

Related questions
See all questions in Equations of Parallel and Perpendicular Lines
Impact of this question
1529 views around the world
You can reuse this answer
Creative Commons License