A line passes through #(5 ,6 )# and #(7 ,3 )#. A second line passes through #(2 ,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 · 2018-06-23T04:14:26

#color(blue)("One other point on the second line is " (0, 4)#

#"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (3-6) / (7-5) = -3/2#

As #2^(nd)# line is parallel to the first line, slope of second line also #-3/2#

#"Equation of second line in point - slope form is "

#(y - 1) = -(3/2) * (x - 2)#

#2y - 2 = -3x + 6#

#3x + 2y = 8#

Let x = 0. Then y = 4#

#color(blue)("One other point on the second line is " (0, 4)#