# A line passes through #(5 ,8 )# and #(2 ,9 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Parallel lines have the same slope.

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To find a point that the second line may pass through if it is parallel to the first line, we need to use the slope of the first line. The slope of a line passing through points ((x_1, y_1)) and ((x_2, y_2)) is given by (\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}).

Using the given points (5, 8) and (2, 9) for the first line, the slope is (\frac{9 - 8}{2 - 5} = -\frac{1}{3}).

Since the second line is parallel to the first line, it will have the same slope of (-\frac{1}{3}). Using the point (3, 5) on the second line and the slope, we can find the y-intercept (b) using the point-slope form of a line equation: (y = mx + b), where (m) is the slope.

Substituting the slope (-\frac{1}{3}) and point (3, 5) into the equation gives: [5 = -\frac{1}{3} \times 3 + b] [5 = -1 + b] [b = 6]

So, the equation of the second line is (y = -\frac{1}{3}x + 6).

Now, to find another point on this line, we can choose any x-value and solve for y. For example, let's choose (x = 0): [y = -\frac{1}{3} \times 0 + 6] [y = 6]

Therefore, another point that the second line may pass through is (0, 6).

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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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