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In the rectangular coordinate system, if the line x = 2y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p ?

A. -2 B. 0 C. 1/2 D. 1 E. 2

The line x = 2y + 5 passes through points (m,n) and (m + 2,n + p) means that m=2n+5 and m+2=2(n+p)+5. Now, subtract the first equation from the second: (m+2)-m=2(n+p)+5-(2n+5) --> 2=2p --> p=1.

Re: In the rectangular coordinate system, if the line x = 2y + 5 [#permalink]

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12 Oct 2013, 17:19

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Re: In the rectangular coordinate system, if the line x = 2y + 5 [#permalink]

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18 Mar 2015, 17:37

Hello from the GMAT Club BumpBot!

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When dealing with a graphing question, it often helps to convert any equations you've been given into "slope-intercept" format (and you might find it helpful to physically draw the graph so you can see it).

Here, we're given the line X = 2Y = 5. Converting that into slope-intercept gives us:

2Y = X - 5

Y = X/2 - 5/2

We're then told that the line passes through the points (M,N) and (M+2,N+P). We're asked for the value of P.

Since we have the line, we can TEST a set of co-ordinate for (M,N)

IF..... X = 0 Y = -5/2

So (M,N) is the point (0, -5/2)

The second point is (M+2,N+P)

Since our M = 0......M+2 = 2..... we have to see what happens when....

X = 2 Y = 1 - 5/2 = -3/2

So (M+2,N+P) is the point (2, -3/2)

So between the first point and the second point, what has happened to the Y co-ordinate? It went from -5/2 to -3/2, so it INCREASED by 1.

Re: In the rectangular coordinate system, if the line x = 2y + 5 [#permalink]

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14 Jul 2016, 04:15

macjas wrote:

In the rectangular coordinate system, if the line x = 2y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p ?

A. -2 B. 0 C. 1/2 D. 1 E. 2

If 2y+5=x then, 2y=x-5 or \(y=\frac{x}{2}-\frac{5}{2}\)

Now this has become the equation of line in the point slope form. {y=mx+b} slope (m) is 1/2 and we also know Slope (m)=\(\frac{y2-y1}{x2-x1}\)

threfore putting the value of x and y from the question we get \(\frac{n+p-n}{m+2-m} = \frac{1}{2}\)

\(\frac{p}{2}=\frac{1}{2}\) ===> p=1

ANSWER IS D
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Re: In the rectangular coordinate system, if the line x = 2y + 5
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14 Jul 2016, 04:15

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