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).

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