A line passes through #(3 ,4 )# and #(4 ,7 )#. A second line passes through #(7 ,9 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Aviv S.
Jan 26, 2018

Any point on the line #y = 3x-12# is a viable answer.

Explanation:

Slope formula from two points:

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

Slope of the given line:

#m = (7-4)/(4-3)=3/1=3#

The equation of this line using point-slope form:

#y-y_1=m(x-x_1)=>#

#y-7=3(x-4)#

#y-7=3x-12#

#y=3x-5#

Since the unknown line is parallel to this one, it has the same slope. Using the newfound slope, we can craft an equation for the new line:

#y-y_1=m(x-x_1)=>#

#y-9=3(x-7)#

#y-9=3x-21#

#y=3x-12#

This is the "second line" that the question mentions. Now, we just need to pick a point anywhere on this line by plugging in an #x#-value and get a #y#-value back. I'll pick 6 for an #x#-value:

#y=3x-12=>#

#y=3(6)-12#

#y=18-12#

#y=6#

A point on the line is #(6, 6)#.

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