A line passes through #(2 ,8 )# and #(4 ,5 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Vinay K.
Nov 28, 2016

#(0,9.5) and (19/3,0)#

Explanation:

Parallel lines have same slope/gradient.

Slope of first line = #m# = #[(y_2 - y_1)/(x_2 - x_1)]#

= #[(5-8)/(4-2)]# = #(-3/2)#

Therefore slope of another line is too #-(3/2)#.

Equation of another line :

#(y - y_1) = m (x - x1)#

#(y - 5) = -3/2 (x - x_1)#

#2 xx (y - 5) = -3 xx (x-3)#

#2y - 10 = -3x +9#

#2y + 3x = 19#

Now by trial and error method we can put two values of #x and y# such that these values satisfy the above equation. Best way is to put #x = 0# and # y =0#.

So the other points could be

(0,9.5) and (#19/3#, 0)

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