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

Any point on the line

Slope formula from two points:

Slope of the given line:

The equation of this line using point-slope form:

Since the unknown line is parallel to this one, it has the same slope. Using the newfound slope, we can craft an equation for the new line:

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Since the second line is parallel to the first line, it will have the same slope as the first line.

The slope of the first line passing through (3, 4) and (4, 7) is given by:

[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 4}{4 - 3} = \frac{3}{1} = 3 ]

Therefore, the second line passing through (7, 9) and parallel to the first line will also have a slope of 3.

Using the point-slope form of a linear equation, the equation of the second line passing through (7, 9) with slope 3 is:

[ y - 9 = 3(x - 7) ]

Expanding this equation gives:

[ y - 9 = 3x - 21 ]

[ y = 3x - 12 ]

To find another point on this line, we can choose any value of ( x ) and calculate the corresponding ( y ). Let's choose ( x = 0 ):

[ y = 3(0) - 12 ]

[ y = -12 ]

Therefore, another point that the second line may pass through is (0, -12).

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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 ,8 )# and #( 1, 5 )#. A second line passes through #( 6, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- How do we find out whether four points #A(3,-1,-1),B(-2,1,2)#, #C(8,-3,0)# and #D(0,2,-1)# lie in the same plane or not?
- A triangle has corners at #(5 ,1 )#, #(7 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?
- What is the perimeter of a triangle with corners at #(3 ,6 )#, #(1 ,5 )#, and #(2 ,1 )#?
- Circle A has a center at #(8 ,-1 )# and a radius of #3 #. Circle B has a center at #(-2 ,-2 )# and a radius of #7 #. Do the circles overlap? If not, what is the smallest distance between them?

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