# A line passes through #(2 ,5 )# and #(0 ,1 )#. A second line passes through #(7 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

First, find the slope of the first line.

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If the second line is parallel to the first line, it means their slopes are equal. To find the slope of the first line passing through the points (2, 5) and (0, 1), we use the formula:

[ m = \frac{y_2 - y_1}{x_2 - x_1} ]

[ m = \frac{1 - 5}{0 - 2} = \frac{-4}{-2} = 2 ]

Now, as the second line is parallel to the first, its slope should also be 2. Using the point-slope form of a line, we can write the equation of the second line passing through the point (7, 1) as:

[ y - 1 = 2(x - 7) ]

Expanding this equation, we get:

[ y - 1 = 2x - 14 ]

[ y = 2x - 13 ]

To find another point on this line, we can pick any value of x and substitute it into the equation to solve for y. Let's choose x = 0:

[ y = 2(0) - 13 ]

[ y = -13 ]

So, another point that the second line may pass through is (0, -13).

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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.

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.

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.

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