A line passes through #(1 ,5 )# and #(8 ,3 )#. A second line passes through #(7 ,6 )#. 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 · 2018-06-23T06:31:29

#color(green)("One other point on the second line is " (21,2)#

#"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (3-5) / (8-1) = -2/7#

As #2^(nd)# line is parallel to the first line, slope of second line also #-2/7#

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

#(y - 6) = -2/7 * (x - 7)#

#7y - 42 = -2x + 14#

#2x + 7y = 56#

Let y = 2. Then x = 21#

#color(green)("One other point on the second line is " (21,2)#