# A line passes through #(5 ,6 )# and #(7 ,3 )#. A second line passes through #(2 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Using point slope form of a line:

Using point slope form of a line:

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To find a point that the second line may pass through if it's parallel to the first line passing through (5,6) and (7,3), we can use the same slope as the first line.

The slope of the first line is given by: [ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ]

Substituting the given points (5,6) and (7,3) into the equation, we get: [ m = \frac{{3 - 6}}{{7 - 5}} = \frac{{-3}}{{2}} ]

Now, for the second line to be parallel, it must have the same slope. So, using the point-slope form of a line equation: [ y - y_1 = m(x - x_1) ] [ y - 8 = -\frac{3}{2}(x - 2) ]

Expanding and rearranging, we get: [ y - 8 = -\frac{3}{2}x + 3 ] [ y = -\frac{3}{2}x + 11 ]

To find another point, we can choose any value for ( x ) and solve for ( y ). Let's take ( x = 0 ): [ y = -\frac{3}{2}(0) + 11 ] [ y = 11 ]

So, another point on the second line could be (0,11).

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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 triangle has corners at #(4 ,4 )#, #(8 ,6 )#, and #(7 ,1 )#. How far is the triangle's centroid from the origin?
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- A triangle has corners at #(6 ,7 )#, #(2 ,6 )#, and #(1 ,2 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(7 ,5 )# and an area of #92 pi#. Circle B has a center at #(9 ,2 )# and an area of #14 pi#. Do the circles overlap?
- An isosceles triangle has sides #a,# #b,# and #c# with sides #a# and #c# being equal in length. If side #b# goes from #(5 ,1 )# to #(3 ,2 )# and the triangle's area is #8 #, what are the possible coordinates of the triangle's third vertex?

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