Line P and Q intersect at a point (2,-5), is the slope of line P is

Question

Line P and Q intersect at a point (2,-5), is the slope of line P is greater than that of line Q?

(1) X intercept of P is less than Q

(2) Y intercept of P is more than Q.

stne · Answer

y = mx+c

m= \frac{y-c}{x}

m= \frac{-5-c}{2}   (  x=2  and   y = -5   given)

Hence we need  c  or  y  - intercept to find the value of the slope.

(1) X intercept of P is less than Q

Not what we are looking for,  CANNOT   give the value of the slope.
 
INSUFF.

(2) Y intercept of P is more than Q.

Exactly what we are looking for.

As the value of  c  increases slope will decrease. Hence slope of  p  is  less than   slope of  q.

SUFF.

Ans B

Hope it's clear.

thakurarun85 · Answer

The answer will be D.

the equation of line is x/a+y/b=1 a and b are x intercept and y intercept.

slope = -b/a

also when using

y=mx+c

x intercept = -c/m hence y/c= x -x intercept => -5/c= 2-(x intercept) => c= -c/(2-xintercept) when

So x intercept is small the slope is small.

The answer is D.

rudi0setyawan · Answer

I don't understand why it's not D?
Statement (2) suff, I get it.

But why (1) insuff?
If we know the x intercept (0,y) dont this means we can find the slope? (and which is greater too..)

Bunuel · Answer

For (1) consider the following example: If P is y = 2x - 9 and Q is y = x - 7, then the slope of P (2) is more than that of Q (1). https://gmatclub.com/forum/download/file.php?id=69907 If P is y = -2x - 1 and Q is y = x - 7, then the slope of P (-2) is less than that of Q (1). https://gmatclub.com/forum/download/file.php?id=69905 desmos-graph (1).png desmos-graph.png

Can,Will · Answer

dear experts please suggest my approach is correct or not

TBT · Answer

Can you show a similar example for option B too.

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=70225 Check the image above. Line Q's y-intercept will be somewhere in the red region of y axis. Q will pass through that point and (2,-5), so the slope of Q would in any case be positive (it goes from bottom left to up right) and it will be steeper than line P, thus the slope of Q will be more than that of P. Hope it's clear. 2.png

rickyric395 · Answer

Hey Bunuel, for statement B, there can still be a cases when y intercept of line P is greater than Q and slope of P can be greater than Q and opposite can be true too i.e slope of P less than Q, so how can we be sure of B?

Bunuel · Answer

Please show a drawing proving your point. Thank you!

rickyric395 · Answer

Posting a separate comment as quoting can be done max 3 times.
Hey Bunuel, I made a mistake, I considered only absolute values , eg- Q passes through (0,4) and P passes through (0,8) then absolute of slope(P > Q). but in that case, slopes would be -ve and hence Q's slope will always be greater.
Thanks .

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Line P and Q intersect at a point (2,-5), is the slope of line P is

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Line P and Q intersect at a point (2,-5), is the slope of line P is

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