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

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

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

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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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.

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

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

The equation can be re-arranged as x-2y-5=0. So, with reference to straight line equation ax+by+c=0, here a=1, b=-2. The slope of a straight line = -a/b, therefore in this case -1/(-2)=1/2.
No, the slope between the given points = (y2-y1)/(x2-x1)={(n+p)-n}/{(m+2)-m}=p/2

Therefore, p/2=1/2, or p=1

Slope of the line is 1/2 =y/x i.e. for every increase in x by 2, y will increase by 1 (1)
slope =rise/lead=y/x
(m,n)=(x,y)
(m+2,n+p)=(x+2,y+p) from (1) increase in x by +2 will lead to increase of y by +1
Therefore P=1

(m + 2) = 2 (n + p) + 5
=> m = 2n + 2p + 3

Compared to the given formular with (m,n)

m = 2n + 5

2p + 3 = 5

=> p=1

So answer D