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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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15 Mar 2015, 22:06
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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16 Mar 2015, 21:09
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Bunuel wrote: Attachment: 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 Kudos for a correct solution.I am surprised no one has solved this question yet! Using the slope concept, if x coordinate increases by 7 (from (– 5, – 1) to (2, 2)), y coordinate increases by 3 (from 1 to 2). So when x coordinate increases by further 3 (from 2 to 5), the y coordinate will increase by (3/7)*3 = 9/7 = 1 (2/7) So y coordinate will become 2 + 1(2/7) = 3 (2/7) Answer (C)
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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17 Mar 2015, 08:50
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Here is my approach:
m= 2+1 / 2+5 = 3/7
y = (3/7)x + b 2 = (3/7)2 + b b = 8/7
y = (3/7)5 + (8/7) y = 23/7 = 3 2/7
Answer: C



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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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22 Mar 2015, 08:44
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Bunuel wrote: Attachment: 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 Kudos for a correct solution.Oops , i am missing a chance to earn a easy kudo . here we go , Slope of line when calculated with (5,1) (2,2) = \(3/7\) Slope of line when calculated with (2,2) (5,q) = \(\frac{q2}{52}\) \(\frac{q2}{3} = \frac{3}{7}\) \(q= 3 \frac{2}{7}\)
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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22 Mar 2015, 11:04
C
slopes are same for all the points
so we can equate the slope3/7 to the one with Q coordianare
getting 23/7



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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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23 Mar 2015, 04:33
Bunuel wrote: 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 Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:Think about this visually. From (–5, –1) to (2, 2), the line moves right 7 and up 3, so that’s a slope of 3/7. From the point (2, 2) to the point (5, Q), there’s a horizontal distance of 3, an unknown vertical distance — call it h, so that h = Q – 2, or Q = h + 2. The ratio of this vertical and horizontal distance must equal the slope. h/3 = 3/7 > h = 9/7. That’s h. Now, add 2 to get Q. Q = h + 2 = 3 2/7. Answer = (C)
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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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13 May 2015, 09:10
Let the 3 points be A(5, 1) B(2, 2) and C(5, Q). Equation of line passing through A and B is : (yy1) = M(xx1) y + 1 = 3/7( x + 5) .. here slope(M) is calculated as : y2  y1/x2 x1( gives 3/7) Since point C(5, Q) passes through the line, so it should satisfy the above equation. Q + 1 = 3/7 (5 + 5) Q = 30/7  1 Q = 23/7 or 3 2/7 Option C
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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25 Feb 2017, 05:54
As slope for the line remains constant, slope between (5,1) and (2,2) would be the same. thus, {2 (1)}/{2(5)} = (Q2)/(52) => 3/7=(Q2)/3 => Q2=9/7 => Q=23/7 = 3 2/7



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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]
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09 Apr 2017, 23:38
VeritasPrepKarishma wrote: Bunuel wrote: Attachment: 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 Kudos for a correct solution.I am surprised no one has solved this question yet! Using the slope concept, if x coordinate increases by 7 (from (– 5, – 1) to (2, 2)), y coordinate increases by 3 (from 1 to 2). So when x coordinate increases by further 3 (from 2 to 5), the y coordinate will increase by (3/7)*3 = 9/7 = 1 (2/7) So y coordinate will become 2 + 1(2/7) = 3 (2/7) Answer (C) Responding to a pm: Quote: I really did not understand how did u get 2 ahead of 9/7. Also, the concept of slopes that you used, can u explain it to me. I do understand that slopes is rise/ run. or I have read it in school as Tan angle that line makes with x axis. Now, the approach you used I drew inference that Slope is with an increase in an x coordinate the y coordinate increases with according to slope .
If you write \(\frac{9}{7}\) in mixed fractions, you get \(1\frac{2}{7}\). As for the slope concept, I have explained it in detail in this blog post: https://www.veritasprep.com/blog/2016/0 ... linegmat/Take a look and get back to me if any doubts remain.
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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What
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