Question

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B. Which equation represents Grant’s path? y = 2 – 4x y = 4 – y = 6 – y = 8 – 2x

Answer 1

From the diagram above you can see that points A and B have coordinates (8,0) and (-4,6), respectively.

The equation of the line passing through the pointa A and B is:

$y-y_A=\dfrac{y_B-y_A}{x_B-x_A}(x-x_A).$

Then

$y-0=\dfrac{6-0}{-4-8}(x-8),\\ \\y=-\dfrac{6}{12}(x-8),\\ \\y=-\dfrac{1}{2}(x-8),\\ \\y=-\dfrac{1}{2}x+4.$

Answer: $y=4-\dfrac{1}{2}x.$

Answer 2

Answer:

y = 4 – x/2

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