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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

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by BTGmoderatorDC » Mon Mar 23, 2020 6:06 pm

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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2


OA C

Source: Magoosh
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

by Scott@TargetTestPrep » Sat Mar 28, 2020 3:16 pm
BTGmoderatorDC wrote: ↑
Mon Mar 23, 2020 6:06 pm
 ppocg_img3.png

Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2


OA C

Source: Magoosh
Since the slope of the line has to be the same no matter which pair of points we use to determine the slope, we can create the equation:

(2 - (-1)) / (2 - (-5)) = (Q - 2) / (5 - 2)

Notice that on the left hand side of the equation, we use the points (2, 2) and (-5, -1) to determine the slope and on the right hand side, we use the points (5, Q) and (2, 2) to do so. Now, solving the equation, we have:

3/7 = (Q - 2)/3

7(Q - 2) = 3(3)

7Q - 14 = 9

7Q = 23

Q = 23/7 = 3 2/7

Answer: C

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