# A line passes through #(9 ,3 )# and #( 3, 5 )#. A second line passes through #( 7, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Parallel lines have the same slope.

Get the slope using the points passed through by the first line

Get the equation of the second line

Substitute the point passed through by the second line to get the y-intercept

Hence, the equation of the second line is

Hence, we have

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If the second line is parallel to the first line, it will have the same slope as the first line.

The slope of the first line passing through (9, 3) and (3, 5) is:

[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{3 - 9} = \frac{2}{-6} = -\frac{1}{3} ]

Since the second line is parallel, it will also have a slope of -1/3. Using the point-slope form of a linear equation ((y - y_1) = m(x - x_1)), where (m = -\frac{1}{3}) and ((x_1, y_1) = (7, 8)), we can find another point on the second line:

[ (y - 8) = -\frac{1}{3}(x - 7) ]

[ y - 8 = -\frac{1}{3}x + \frac{7}{3} ]

[ y = -\frac{1}{3}x + \frac{7}{3} + 8 ]

[ y = -\frac{1}{3}x + \frac{31}{3} ]

Therefore, another point on the second line is (0, 31/3).

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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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