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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, 22:12

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 [#permalink]

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27 Jun 2012, 22:39

2

This post received KUDOS

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 [#permalink]

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16 Feb 2015, 06:57

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 [#permalink]

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14 Jul 2016, 04:25

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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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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