# A line passes through #(1 ,5 )# and #(8 ,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?

I didn't use math to figure this out, but I'll explain both ways. First the easy way.

You end up with

(I kept the fractions so it would be easier to solve).

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To find another point that the second line may pass through if it is parallel to the first line, we use the concept that parallel lines have the same slope.

First, we find the slope of the first line passing through points (1, 5) and (8, 7). The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Using the given points: m = (7 - 5) / (8 - 1) m = 2 / 7

Now, since the second line is parallel to the first line, it must have the same slope. Thus, the second line passing through the point (3, 6) and having the same slope of 2/7 can be found by substituting the slope and one point into the point-slope form of a line.

The point-slope form of a line is: y - y1 = m(x - x1)

Substituting the values: y - 6 = (2/7)(x - 3)

Now, we can solve for y to find the equation of the second line. We can also choose any value for x to find the corresponding y-coordinate. For simplicity, let's choose x = 0:

y - 6 = (2/7)(0 - 3) y - 6 = (2/7)(-3) y - 6 = -6/7 y = -6/7 + 6 y ≈ 41/7

So, one other point that the second line may pass through, given that it is parallel to the first line, is approximately (0, 41/7) or (0, 5.857).

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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.

- What is the perimeter of a triangle with corners at #(7 ,3 )#, #(4 ,5 )#, and #(3 ,3 )#?
- Circle A has a center at #(-5 ,8 )# and a radius of #4 #. Circle B has a center at #(-3 ,3 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(2 ,5 )# to #(8 ,7 )# and the triangle's area is #12 #, what are the possible coordinates of the triangle's third corner?
- What is the perimeter of a triangle with corners at #(3 ,7 )#, #(1 ,3 )#, and #(4 ,9 )#?
- Circle A has a center at #(-1 ,2 )# and a radius of #2 #. Circle B has a center at #(5 ,-4 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?

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