# A line passes through #(4 ,9 )# and #(1 ,6 )#. A second line passes through #(3 ,7 )#. What is one other point that the second line may pass through if it is parallel to the first line?

(0,4)

First of all, both of the lines are parallel to each other, meaning they have the same slope

To find the slope, we use the slope formula:

Plug in the numbers from the points of the 2 lines, and find the slope of both lines

The 1 is the slope of both of the lines, as parallel lines have the same slope.

Now, we can use the point-slope formula to get the slope-intercept equation of the second line

Plug in the numbers, and get the new formula

Now, we can get a second point for the second line: the y-intercept. To find the y-intercept, plug in 0 for the x value of the equation, and simplify. The resulting point found should be your new answer:

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To find a point through which the second line passes, we need to maintain the same slope as the first line, since the lines are parallel. The slope of the first line passing through (4,9) and (1,6) is (9-6)/(4-1) = 3/3 = 1. So, the second line should also have a slope of 1. Therefore, if the second line passes through (3,7), one other point it may pass through is (4,8).

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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 line passes through #(2 ,9 )# and #(5 ,2 )#. A second line passes through #(3 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Circle A has a center at #(1 ,4 )# and an area of #28 pi#. Circle B has a center at #(7 ,9 )# and an area of #8 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- Circle A has a center at #(6 ,5 )# and an area of #6 pi#. Circle B has a center at #(12 ,7 )# and an area of #48 pi#. Do the circles overlap?
- How are parallel and perpendicular lines alike?
- Circle A has a center at #(6 ,4 )# and a radius of #3 #. Circle B has a center at #(-1 ,6 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

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