A line passes through #(9 ,3 )# and #( 3, 5 )#. A second line passes through #( 7, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Dec 4, 2016

#(0, 17)#

Explanation:

Parallel lines have the same slope.

Get the slope using the points passed through by the first line

#m = (y_1 - y_2)/(x_1 - x_2)#

#P_1: (9, 3)#
#P_2: (3, 5)#

#=> m = (3 - 5)/(9 - 3)#

#=> m = -2/6 = -1/3#


Get the equation of the second line

#y = mx + b#

#y = -1/3x + b#

Substitute the point passed through by the second line to get the y-intercept

#P_1': (7, 8)#

#8 = -1/3(7) + b#

#24 = -7 + b#

#b = 17#

Hence, the equation of the second line is

#y = -1/3x + 17#


To determine another point that the line passes through, simply select a desired value for either #x# or #y#. Substitute the desired value into the equation to get its corresponding #y# (or #x#).

For simplicity, let's use #x = 0#.

#y = -1/3(0) + 17#

#y = 17#

Hence, we have

#P_2': (0, 17)#