A line passes through #(2 ,8 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
smendyka
Aug 18, 2017

See a solution process below:

Explanation:

First, we need to determine the slope of the first line. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(5) - color(blue)(8))/(color(red)(3) - color(blue)(2)) = (-3)/1#

Because the two lines in the problem are parallel by definition they have the same slope.

A slope of #(-3)/1# means it has a rise of #-3# and a run of #1#. Or, in other words, for each #1# unit the line moves to the right on the #x# axis it moves down #3# units on the #y# axis.

We can find another point on the second line by adding #1# to the #x# coordinate and subtracting #3# from the #y# coordinate:

#(4 + 1, 8 - 3) => (5, 5)#

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