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In a dream, Blair is confined to a coordinate plane, moving along a line with a constant speed. Blair’s position at 4 am is (2, 5) and at 6 am it is (6, 3). What is Blair’s position at 8:15 am when the alarm goes off?

Answer :

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Answer:

(10.5, 0.75)

Explanation:

In order to perform this exercise we first need to define the equation of the line

So,

[tex]y = mx + b[/tex]

[tex]m = \frac{(y1-y2)} { (x1-x2)} = \frac{2-6} {3-5} = - 1/2[/tex]

So,

[tex]y = -\frac{1}{2}x + b[/tex]

In the first coordinate we can identify b replacing,

[tex]5 = -\frac{1}{2}(2) + b[/tex]

[tex]5 = -1 + b[/tex]

[tex]b = 6[/tex]

Since in 2 Hrs Blair moves a distance of 4 in the horizontal and

Since in 1 Hr Blair would travel a distance of 2 you have,

[tex]4.25 * 2 = 8.5[/tex]

[tex]8.5 + 2 = 10.5[/tex]

[tex]y = -\frac{1}{2} (10.5) + 6[/tex]

[tex]y = -5.25 + 6 = 0.75[/tex]

Blair's position at 8:15 am would be (10.5, 0.75)

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