A line passes through #(4 ,7 )# and #(6 ,4 )#. 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?

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Answer 1 · 2018-06-23T06:17:13

#color(crimson)("One other point on the second line is " (3, 5)#

#"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (4-7) / (6-4) = -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 - 5) = -3/2 * (x - 3)#

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

#3x + 2y = 19#

Let y = 5. Then x = 3#

#color(crimson)("One other point on the second line is " (3, 5)#