# A line passes through #(3 ,6 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. 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, then they have the same slope. The slope of the first line passing through (3, 6) and (6, 5) can be calculated as follows:

(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 6}{6 - 3} = \frac{-1}{3})

Since the second line is parallel to the first line, it will also have a slope of -1/3.

Now, we have the slope and one point (4, 3) of the second line. We can use the point-slope form of the equation of a line to find other points on the second line.

Using the slope-intercept form:

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

Substituting the values (m = -\frac{1}{3}), (x_1 = 4), and (y_1 = 3), we get:

(y - 3 = -\frac{1}{3}(x - 4))

Expanding and simplifying:

(y - 3 = -\frac{1}{3}x + \frac{4}{3})

(y = -\frac{1}{3}x + \frac{13}{3})

Now, we can choose any value of x and calculate the corresponding y-coordinate to find other points on the line. For example, let's choose another x-value, say x = 2:

(y = -\frac{1}{3}(2) + \frac{13}{3})

(y = -\frac{2}{3} + \frac{13}{3})

(y = \frac{11}{3})

So, the point (2, 11/3) lies on the second line parallel to the first line passing through (3, 6) and (6, 5).

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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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- What is the perimeter of a triangle with corners at #(3 ,5 )#, #(1 ,6 )#, and #(4 ,3 )#?
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- Circle A has a center at #(5 ,4 )# and an area of #15 pi#. Circle B has a center at #(2 ,1 )# and an area of #90 pi#. Do the circles overlap?
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