# A line passes through #(5 ,0 )# and #(7 ,9 )#. 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?

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If the second line is parallel to the first line passing through (5,0) and (7,9), it must have the same slope as the first line. The slope of the first line can be found using the formula:

(m = \frac{{y_2 - y_1}}{{x_2 - x_1}})

Substituting the coordinates (5,0) and (7,9) into the formula, we get:

(m = \frac{{9 - 0}}{{7 - 5}} = \frac{9}{2})

So, the slope of the second line must also be (\frac{9}{2}) to be parallel.

Using the point-slope form of a line (y - y_1 = m(x - x_1)), where ((x_1, y_1)) is a point on the line and (m) is the slope, and substituting the given point (3,6) and the slope (\frac{9}{2}), we can find the equation of the second line:

(y - 6 = \frac{9}{2}(x - 3))

Expanding and rearranging, we get:

(y = \frac{9}{2}x - \frac{27}{2} + 6)

(y = \frac{9}{2}x - \frac{15}{2})

To find another point on this line, we can choose any value of (x) and solve for (y). Let's take (x = 1) for simplicity:

(y = \frac{9}{2}(1) - \frac{15}{2} = \frac{9}{2} - \frac{15}{2} = -3)

Therefore, another point on the second line is (1, -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.

- What are two lines in the same plane that intersect at right angles?
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- Are the planes #x+y+z=1# , #x-y+z=1# parallel, perpendicular, or neither? If neither, what is the angle between them?
- Circle A has a center at #(5 ,1 )# and an area of #23 pi#. Circle B has a center at #(2 ,8 )# and an area of #15 pi#. Do the circles overlap?
- A triangle has corners at #(9 ,3 )#, #(7 ,5 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

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