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

[BTGmoderatorDC]

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

[Scott@TargetTestPrep]

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