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

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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


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.

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

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

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

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New post 18 Mar 2015, 20:23
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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

Final Answer:
[Reveal] Spoiler:
D


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

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New post 16 Jun 2015, 12:35
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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


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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New post 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   [#permalink] 14 Jul 2016, 04:15
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