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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.

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12 Oct 2013, 17:19

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18 Mar 2015, 17:37

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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

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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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Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

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

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04 Nov 2016, 06:17

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EMPOWERgmatRichC wrote:

Hi All,

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.

I have been doing the EMPOWERgmat prep for the last month and I have already seen an improvement. You focus on very simple methods of breaking problems down. I'm not quite an assassin yet but I have to be soon. Thanks for the help.

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

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23 Jan 2017, 01:36

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

Since the line x = 2y + 5 passes through points (m,n) and (m + 2,n + p) we have m=2n+5 --------- I m+2=2(n+p)+5. --------- II solving I and II we have p =1 Hence option D is correct.

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

We are given that line x = 2y + 5 passes through points (m,n) and (m + 2,n + p). Thus, we can make two equations and substitute m and m + 2 for x, and n and n + p for y.

Equation 1: The ordered pair (m,n) means that x = m and y = n. Substitute these values into the equation x = 2y + 5.

m = 2n + 5

Equation 2: The ordered pair (m + 2,n + p) means that we will let x = m + 2 and y = n + p.

m + 2 = 2(n + p) + 5

m + 2 = 2n + 2p + 5

m = 2n + 2p + 3

We can equate equations 1 and 2 and we have:

2n + 5 = 2n + 2p + 3

5 = 2p + 3

2 = 2p

p = 1

Alternate solution:

We are given that line x = 2y + 5 passes through points (m,n) and (m + 2,n + p). We can find the slope of the line by isolating y:

x = 2y + 5

2y = x - 5

y = 1/2x - 5/2

Thus, the line has slope 1/2. For any two points on this line, the slope between these two points must be 1/2 also. Since (m,n) and (m + 2,n + p) are on the line, the slope of the line connecting them must be 1/2. Therefore, using the slope formula, which is slope = (change in y)/(change in x), we have:

(n + p - n)/(m + 2 - m) = 1/2

p/2 = 1/2

p = 1

Answer: D
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