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?

1 Answer
Apr 18, 2018

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

Explanation:

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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