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

there are an infinite number of points you could select from that line not including the given point (3, 6) but the y intercept would be a very convenient one since it is the point (0, 4) and can be readily determined from the equation.

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If the second line is parallel to the first line passing through points (4, 9) and (1, 7), then it must have the same slope as the first line. To find the slope of the first line, we use the formula:

[ \text{Slope} = \frac{{\text{change in } y}}{{\text{change in } x}} ]

For the first line passing through (4, 9) and (1, 7):

[ \text{Slope} = \frac{{7 - 9}}{{1 - 4}} = \frac{{-2}}{{-3}} = \frac{2}{3} ]

Since the second line is parallel to the first line, it must have the same slope. Now, using the point (3, 6) and the slope ( \frac{2}{3} ), we can find the equation of the second line using the point-slope form:

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

[ y - 6 = \frac{2}{3}(x - 3) ]

Solving this equation for ( y ), we get:

[ y = \frac{2}{3}x + 4 ]

So, any point that satisfies this equation will lie on the second line parallel to the first line.

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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 #(0 ,5 )# and #(8 ,3 )#. 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?
- A triangle has corners at #(4 ,3 )#, #(2 ,6 )#, and #(1 ,5 )#. How far is the triangle's centroid from the origin?
- For line #ST#, the coordinates of point #T# are T(0,4). The midpoint of ST is (5, -8). What are the coordinates of point #S#?
- Circle A has a center at #(2 ,4 )# and a radius of #9 #. Circle B has a center at #(1 ,-5 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
- A line passes through #(4 ,9 )# and #(8 ,7 )#. A second line passes through #(2 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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