A line passes through #(5 ,6 )# and #(7 ,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?

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Answer 1 · 2018-04-18T12:24:51

# (10 ,4 )# is other point through which second line passes.

The slope of the line passing through #(5,6) and (7,8)# is

#m= (y_2-y_1)/(x_2-x_1)= (8-6)/(7-5)=2/2=1#

Parallel lines have equal slopes . Therefore the slope of second

line is also #m=1#

The equation of line passing through

#(x_1,y_1)# having slope of #m# is #y-y_1=m(x-x_1)#.

The equation of line passing through #(7,1)# having slope of

#1# is #y-1=1(x-7) or y-1=x-7 or x-y = 6 # ,

choosing #x and y# , satisfying the equation we can have infinite

number of other points , let #x=10# then # y=10-6=4 :.#

# (10 ,4 )# is one such point through which second line passes.

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