# A line passes through #(5 ,0 )# and #(7 ,3 )#. A second line passes through #(3 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?

A point that makes

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If the second line is parallel to the first line passing through points (5, 0) and (7, 3), then the direction of the second line will be the same as that of the first line.

The direction of the first line can be found by calculating the slope using the given points:

[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}] [m = \frac{{3 - 0}}{{7 - 5}}] [m = \frac{3}{2}]

Since the second line is parallel to the first line, it will have the same slope. Now, using the given point (3, 6) and the slope (m = \frac{3}{2}), we can find the equation of the second line using the point-slope form:

[y - y_1 = m(x - x_1)] [y - 6 = \frac{3}{2}(x - 3)] [y - 6 = \frac{3}{2}x - \frac{9}{2}] [y = \frac{3}{2}x - \frac{9}{2} + 6] [y = \frac{3}{2}x - \frac{9}{2} + \frac{12}{2}] [y = \frac{3}{2}x + \frac{3}{2}]

So, the equation of the second line parallel to the first line and passing through point (3, 6) is (y = \frac{3}{2}x + \frac{3}{2}).

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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.

- A line passes through #(6 ,4 )# and #(9 ,0 )#. A second line passes through #(3 ,4 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A triangle has corners at #(1 ,5 )#, #(9 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(1 ,4 )# to #(5 ,8 )# and the triangle's area is #27 #, what are the possible coordinates of the triangle's third corner?
- A line passes through #(5 ,6 )# and #(2 ,8 )#. 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?
- A triangle has corners at #(5 ,9 )#, #(4 ,1 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?

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