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A line passes through #(2 ,8 )# and #(3 ,9 )#. 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?

Answer 1

Aaliyah Anderson

See the explanantion

#color(blue)("Consider line 1")#

Gradient is the amount of up/down for the amount of along when reading left to right.

The amount of along is the change in the x-axis#->3-2=+1# The amount of up/down is the change in y-axis#->9-8=+1#

The gradient #->(y_2-y_1)/(x_2=x_1) = 1/1 =1#

That is, the amount of change for the x-axis is the same as the amount of change for the y-axis '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Consider line 2")#

Thus for line 2 I chose a change of +3.

So if the first point is #(7,6)# then the second one I chose would be

#(7+3,6+3) = (10,9)#

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Answer 2

Sadie Adams

One other point that the second line may pass through if it is parallel to the first line is (8, 7).

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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.