# A line passes through #(4 ,3 )# and #(2 ,9 )#. 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?

From the slope and the given point, we can determine many points that will make this line parallel, including:

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To find a point through which the second line may pass if it is parallel to the first line, we first need to determine the slope of the first line. Using the formula for slope, which is (change in y) / (change in x), we calculate:

Slope of the first line = (9 - 3) / (2 - 4) = 6 / -2 = -3

Since the second line is parallel to the first line, it will have the same slope. Now, using the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can find the equation of the second line. Let's choose the point (7, 1) from the given point:

y - 1 = -3(x - 7)

Expanding and simplifying:

y - 1 = -3x + 21 y = -3x + 22

Now, to find another point on this line, we can arbitrarily choose a value for x and solve for y. Let's choose x = 5:

y = -3(5) + 22 y = -15 + 22 y = 7

So, the point (5, 7) lies on the second line, which is parallel to the first line passing through (4, 3) and (2, 9).

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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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