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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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27 Jun 2012, 23:12
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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
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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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27 Jun 2012, 23:39
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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,
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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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
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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14 Jul 2016, 05:25
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
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
Answer is B
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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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30 Oct 2017, 13:56
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
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
Answer: D
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions
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?
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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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
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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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 ?
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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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
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two
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03 Sep 2018, 06:58
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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
Key Concept: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of that line.
Given equation: x = 3y - 7 One point ON the line is (a, b) So, we can write: a = 3b - 7
Another point ON the line is (a + 3, b + k) So, we can write: a + 3 = 3(b + k) - 7 Expand: a + 3 = 3b + 3k - 7 Subtract 3 from both sides to get: a = 3b + 3k - 10
We now two equations: a = 3b + 3k - 10 a = 3b - 7
Subtract the bottom equation from the top equation to get: 0 = 3k - 3 Add 3 to both sides: 3 = 3k Solve: k = 1
Answer: D
Cheers, Brent
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Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two &nbs
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03 Sep 2018, 06:58
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74% (01:36) correct 
