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A line passes through #(2 ,3 )# and #( 4, 2 )#. A second line passes through #( 7, 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

Evelyn Arboleda

One other point can have coordinates #(9,3), (13,1),(5,5) # and so on which will give rise to a slope of #m = -1/2#

Parallel lines will have the same slope.

Slope is given by the formula

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

First line will have the slope #m = (3-2) / (2-4) = -1/2#

Second line will also have the same slope #m = -1/2#

#:. m = -1/2 = (y_2 - 4) / (x_2 - 7)#

Hence the second point can have coordinates #(9,3), (13,1),(5,5) # and so on which will give rise to a slope of #m = -1/2#

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Answer 2

Ella Armstrong

One other point that the second line may pass through if it is parallel to the first line is (9, 3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.