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# In the xy-coordinate system,if (a,b) and (a+3, b+k) are two

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Director
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In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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21 Apr 2008, 16:49
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In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=?

A. 9
B. 3
C. 7/3
D. 1
E. 1/3

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Joined: 16 Sep 2007
Posts: 211
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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21 Apr 2008, 17:11
2
1
x=3*y-7
convert to (this step is not necessary but I do it out of habit)
y=(x-7)/3

substitute a and b for x and y
1. b=(a-7)/3

b+k=((a+3)-7)/3
substitute equation 1 for b
(a-7)/3+k=((a+3)-7)/3
(a-7)/3+k=(a-4)/3
a-7+3k=a-4
3k=3
k=1

D
Director
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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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21 Apr 2008, 20:29
2
In the xy-coordinate system, if (a,b) and (a+3,b+k) are
two points on the line defined by the equation
x = 3y - 7, then k =

9
3
7/3
1
1/3

given : y = 1/3x + 7/3

Slope => k/3 = 1/3 i.e K =1
Director
Joined: 03 May 2007
Posts: 829
Schools: University of Chicago, Wharton School
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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21 Apr 2008, 20:45
1
2
In the xy-coordinate system, if (a, b) and (a+3, b+k) are two points on the line defined by the equation
x = 3y - 7, then k =

9
3
7/3
1
1/3

x = 3y - 7
y = 1/3 (x) + 7/3
[(b+k) - b]/ [(a+3) - a] = 1/3
k/3 = 1/3
k = 1

D.
VP
Joined: 10 Jun 2007
Posts: 1394
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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21 Apr 2008, 21:30
1
1
In the xy-coordinate system, if (a,b) and (a+3,b+k) are
two points on the line defined by the equation
x = 3y - 7, then k =

9
3
7/3
1
1/3

slope = (y1-y2)/(x1-x2) = (b+k-b) / (a+3-a) = k/3
y = x/3 + 7/3, so slope = 1/3

k/3 = 1/3
k = 1
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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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27 Jun 2012, 15:36
2
Substitute a & b in place of x & y resp... in the eqn.
a-3b+7=0------(i)

Substitute a+3 & b+k in the place of x & y resp...we'll get
a+3=3(b+k)-7 or,
a-3b-3k+10=0-------(ii)

points on the same line will satisfy the equation so ,

equating (i)&(ii)
a-3b-3k+10=a-3b+7
k=1

Ans- D
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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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27 Jun 2012, 23:10
thevenus wrote:
Substitute a & b in place of x & y resp... in the eqn.
a-3b+7=0------(i)

Substitute a+3 & b+k in the place of x & y resp...we'll get
a+3=3(b+k)-7 or,
a-3b-3k+10=0-------(ii)

Or note here itself that a - 3b + 7 = 0 so 3 - 3k = 0 giving you k = 1
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Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Manager Status: Rising GMAT Star Joined: 05 Jun 2012 Posts: 126 Location: Philippines Concentration: General Management, Finance GPA: 3.22 WE: Corporate Finance (Consulting) Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two [#permalink] ### Show Tags 27 Jun 2012, 23:12 1 thevenus wrote: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=? A. 9 B. 3 C. 7/3 D. 1 E. 1/3 My answer is (D). Here's my approach: We are given two points: (a,b) and (a+3,b+k) We are given an equation of the line: x = 3y - 7 Next step is to convert the equation of the line into slope-intercept form. We will have Y = x/3 + 7/3. Don't forget this step because you might fall into the trap and decide that the slope of the line is 3. This makes the question very GMAT-esque. So the slope of the line is 1/3 Now we know that the equation of the slope of the line is given by: slope = (y2 - y1)/(x2 - x1) ---> Remember, the slope is just "rise" over "run." That's why we have: 1/3 = [ (b+k) - b ] / [ (a+3) - a] The two b's will cancel each other in the numerator and so will the two a's in the denominator We will get 1/3 = k / 3 so 3 / 3 = k k = 1 _________________ Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat. - T. Roosevelt Current Student Joined: 29 Mar 2012 Posts: 317 Location: India GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two [#permalink] ### Show Tags 27 Jun 2012, 23:39 2 Hi, Slope of the line x=3y-7 is 1/3 so, we can equate the slope of the line to the slope of the points = $$\frac {y_2-y_1}{x_2-x_1}$$ or $$\frac {(b+k)-(b)}{(a+3)-a} = \frac 13$$ or $$\frac k3 = \frac 13$$ or k=1, Answer (D), Regards, Intern Joined: 08 Jul 2014 Posts: 1 Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two [#permalink] ### Show Tags 16 Feb 2015, 07:57 Maple wrote: x=3*y-7 convert to (this step is not necessary but I do it out of habit) y=(x-7)/3 substitute a and b for x and y 1. b=(a-7)/3 b+k=((a+3)-7)/3 substitute equation 1 for b (a-7)/3+k=((a+3)-7)/3 (a-7)/3+k=(a-4)/3 a-7+3k=a-4 3k=3 k=1 D x=3*y-7 is not y=(x-7)/3 instead it is y=(x+7)/3 or y=(1/3)x+(7/3) since we know (a,b) and (a+3,b+k) belong to the same line, they must have the same slope, 1/3. [(b+k)-b]/[(a+3)-a]=1/3 k/3=1/3 k=1 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12176 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two [#permalink] ### Show Tags 16 Feb 2015, 19:16 2 Hi All, This question can be solved by TESTing VALUES: We're given the equation of a line (X = 3Y - 7) and we're told that two points (A, B) and (A+3, B+K) are on this line. We're asked for the value of K. In graphing questions, it sometimes helps to "visualize" the line better if you write the equation in "slope-intercept" format: X = 3Y - 7 3Y = X + 7 Y = X/3 + 7/3 For the first co-ordinate, let's try to keep things simple... X = 0 Y = 7/3 So... A = 0 B = 7/3 For the second co-ordinate, we have ADD 3 to X.... X = 3 Y = 10/3 So.... A+3 = 3 B+K = 10/3 We know from the first co-ordinate that B = 7/3, so K = 3/3 = 1 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Director
Joined: 04 Jun 2016
Posts: 603
GMAT 1: 750 Q49 V43
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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14 Jul 2016, 05:25
In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=?

A. 9
B. 3
C. 7/3
D. 1
E. 1/3

Our equation is x=3y-7
Lets quickly make it a point intercept form ==> 3y-7=x==>3y=x+7==>$$y=\frac{x}{3}+\frac{7}{3}$$
Now we can see the coefficient of x is $$\frac{1}{3}$$, which by definition is the slope
and we know slope =$$\frac{y2-y1}{x2-x1}$$==> $$\frac{1}{3}=\frac{b+k-b}{a+3-a}$$==> 1/3=k/3
therefore k=1

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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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30 Oct 2017, 13:56
In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=?

A. 9
B. 3
C. 7/3
D. 1
E. 1/3

Recall that an ordered pair represents a pair of x and y coordinates. Substituting the values from the first ordered pair (a,b) into the equation, we can create the following equation:

a = 3b - 7

Substituting the values from the second ordered pair for x and y into the same equation, we have:

a + 3 = 3(b + k) - 7 → a + 3 = 3b + 3k - 7

If we subtract the first equation from the second, we have:

3 = 3k

1 = k

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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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26 Jan 2018, 14:27
EMPOWERgmatRichC wrote:
Hi All,

This question can be solved by TESTing VALUES:

We're given the equation of a line (X = 3Y - 7) and we're told that two points (A, B) and (A+3, B+K) are on this line. We're asked for the value of K.

In graphing questions, it sometimes helps to "visualize" the line better if you write the equation in "slope-intercept" format:

X = 3Y - 7

3Y = X + 7
Y = X/3 + 7/3

For the first co-ordinate, let's try to keep things simple...
X = 0
Y = 7/3

So...
A = 0
B = 7/3

For the second co-ordinate, we have ADD 3 to X....
X = 3
Y = 10/3

So....
A+3 = 3
B+K = 10/3

We know from the first co-ordinate that B = 7/3, so K = 3/3 = 1

GMAT assassins aren't born, they're made,
Rich

Hi Rich, I know the "7/3" came from rewriting to slope-intercept form, but how did you get from "B = 7/3" to "B+K = 10/3"? I know we added 3 to X, but are we adding 3 to Y too?
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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

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26 Jan 2018, 15:03
Hi OCDianaOC,

Both co-ordinates have to 'fit' the equation Y = X/3 + 7/3

The first co-ordinate is (A, B).... and I TESTed VALUES and used (0, 7/3) to define that co-ordinate. Remember: A = 0 and B = 7/3

The second co-ordinate is (A+3, B+K).... notice how that's the SAME A and B from the first co-ordinate. Thus, we have to add 3 to A (so 3+0 = 3) and plug in X=3 into the equation to get the value of the Y....

When X=3....
Y = X/3 + 7/3
Y = (3/3) + 7/3)
Y = 10/3

Since the second co-ordinate is (A+3, B+K), our prior work makes the co-ordinate (3, 10/3). From the prior work, we see that B = 7/3...
B + K = 10/3
(7/3) + K = 10/3
K = 10/3 - 7/3 = 3/3 = 1

GMAT assassins aren't born, they're made,
Rich
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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Director Joined: 09 Mar 2016 Posts: 749 Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two [#permalink] ### Show Tags 21 Feb 2018, 13:40 gmatsaga wrote: thevenus wrote: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=? A. 9 B. 3 C. 7/3 D. 1 E. 1/3 My answer is (D). Here's my approach: We are given two points: (a,b) and (a+3,b+k) We are given an equation of the line: x = 3y - 7 Next step is to convert the equation of the line into slope-intercept form. We will have Y = x/3 + 7/3. Don't forget this step because you might fall into the trap and decide that the slope of the line is 3. This makes the question very GMAT-esque. So the slope of the line is 1/3 Now we know that the equation of the slope of the line is given by: slope = (y2 - y1)/(x2 - x1) ---> Remember, the slope is just "rise" over "run." That's why we have: 1/3 = [ (b+k) - b ] / [ (a+3) - a] The two b's will cancel each other in the numerator and so will the two a's in the denominator We will get 1/3 = k / 3 so 3 / 3 = k k = 1 How did you figure out that slope is 1/3 from here Y = x/3 + 7/3 slope is x/3 but how should i know value of X ? _________________ In English I speak with a dictionary, and with people I am shy. SC Moderator Joined: 22 May 2016 Posts: 1903 In the xy-coordinate system,if (a,b) and (a+3, b+k) are two [#permalink] ### Show Tags 21 Feb 2018, 21:08 1 alimad wrote: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=? A. 9 B. 3 C. 7/3 D. 1 E. 1/3 $$x = 3y - 7$$ Rewrite in slope-intercept form $$y = mx + b$$ m = slope, b = y-intercept, thus: $$3y = x + 7$$ => $$y = \frac{1}{3}x + \frac{7}{3}$$ Slope = $$\frac{1}{3}$$ Slope is also $$\frac{rise}{run}=\frac{(y_2 - y_1)}{(x_2 - x_1)}$$ We have x-and y-coordinates for two points: (a,b) and (a+3,b+k) Set the slope equation equal to the slope value $$\frac{(b+k)-b}{(a+3)-a}=\frac{1}{3}$$ $$\frac{b+k-b}{a+3-a}=\frac{1}{3}$$ $$\frac{k}{3}=\frac{1}{3}$$ $$3k = 3$$ $$k = 1$$ Answer D _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8184 Location: Pune, India Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two [#permalink] ### Show Tags 21 Feb 2018, 21:13 dave13 wrote: gmatsaga wrote: thevenus wrote: In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=? A. 9 B. 3 C. 7/3 D. 1 E. 1/3 My answer is (D). Here's my approach: We are given two points: (a,b) and (a+3,b+k) We are given an equation of the line: x = 3y - 7 Next step is to convert the equation of the line into slope-intercept form. We will have Y = x/3 + 7/3. Don't forget this step because you might fall into the trap and decide that the slope of the line is 3. This makes the question very GMAT-esque. So the slope of the line is 1/3 Now we know that the equation of the slope of the line is given by: slope = (y2 - y1)/(x2 - x1) ---> Remember, the slope is just "rise" over "run." That's why we have: 1/3 = [ (b+k) - b ] / [ (a+3) - a] The two b's will cancel each other in the numerator and so will the two a's in the denominator We will get 1/3 = k / 3 so 3 / 3 = k k = 1 How did you figure out that slope is 1/3 from here Y = x/3 + 7/3 slope is x/3 but how should i know value of X ? The equation of a line is y = mx + c where m is the slope and c is the y-intercept. So the equation looks like this y = 2x + 4 (m = 2, c = 4) y = x/3 + 5 (m = 1/3, c = 5) etc For more, check out this post: http://www.veritasprep.com/blog/2010/12 ... he-graphs/ _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two &nbs [#permalink] 21 Feb 2018, 21:13
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