# A line passes through #(6 ,2 )# and #(3 ,4 )#. 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?

Some points can be

If a line has to pass through a point given the slope, we can use point-slope equation:

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If the second line is parallel to the first line, it means that their slopes are equal. The slope of the first line passing through points ((6, 2)) and ((3, 4)) can be calculated using the formula:

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

where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points on the line.

For the first line:

[m = \frac{{4 - 2}}{{3 - 6}} = \frac{{2}}{{-3}} = -\frac{2}{3}]

Since the second line is parallel to the first line, it must also have a slope of (-\frac{2}{3}).

Given that the second line passes through point ((7, 8)), we can use the point-slope form of the equation of a line to find another point on the line. The point-slope form is:

[y - y_1 = m(x - x_1)]

where (m) is the slope and ((x_1, y_1)) is a point on the line.

For the second line:

[y - 8 = -\frac{2}{3}(x - 7)]

Now, you can choose any value for (x) and solve for (y) to find another point on the line. Let's choose (x = 10) for example:

[y - 8 = -\frac{2}{3}(10 - 7)]

[y - 8 = -\frac{2}{3}(3)]

[y - 8 = -2]

[y = 8 - 2]

[y = 6]

So, if the second line is parallel to the first line and passes through point ((7, 8)), it will also pass through the point ((10, 6)).

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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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