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

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

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27 May 2012, 08:05
4
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15% (low)

Question Stats:

79% (01:36) correct 21% (02:04) wrong based on 324 sessions

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

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27 May 2012, 08:19
3
6
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

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

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29 May 2012, 06:46
2
Another way: Slope of the line can be calculated...

y=mx+c => y= (1/2)x-5/2 => 1/2=n+p-n/m+2-m =>1/2=p/2 => p=1
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Re: In the rectangular coordinate system, if the line x = 2y + 5  [#permalink]

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18 Mar 2015, 19:23
4
1
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.

Thus, P = 1

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

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16 Jun 2015, 11:35
1
1
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

Rewrite x = 2y + 5 like so: y = 0.5X + 2.5

Plug in Values for m = x:

if m = x = 1, the first point is 1, 3
if m = x = 3, the second point is 3, 4

Therefore n = 3 and n + p = 4. p = 1
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Re: In the rectangular coordinate system, if the line x = 2y + 5  [#permalink]

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14 Jul 2016, 03:15
2
1
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

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

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04 Nov 2016, 05:17
1
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.

Thus, P = 1

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Rich

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

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23 Jan 2017, 00:36
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.
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Re: In the rectangular coordinate system, if the line x = 2y + 5  [#permalink]

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25 Jan 2017, 10:19
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

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

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

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21 Jul 2018, 00:24
Bunuel wrote:
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

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.

Hi pushpitkc how is your gmat prep ? hope bumpy roads, pit stops are already behind you, and there is just highway in front of you

can you break down Bubuel`s solution please i dont understand

how from here x = 2y + 5 passes through points (m,n) and (m + 2,n + p) he concludes that that m=2n+5 and m+2=2(n+p)+5.

i can replace (m,n) and (m + 2,n + p) with x, y, p for example (x,y) and (x + 2, y + p)

have a great weekend
Re: In the rectangular coordinate system, if the line x = 2y + 5 &nbs [#permalink] 21 Jul 2018, 00:24
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