Lines n and p lie in the x-y plane. Is the slope of the line

[Adi]

Lines n and p lie in the x-y plane. Is the slope of the line n less than the slope of line p?
1. lines n and p intersect at (5,1)
2. the y-intercept of line n is greater than y-intercept of line p

I chose answer E but the GMAT prep says that the answer is C

In that case I am not using the concept of y-intercept correctly. Could you please explain what I am missing?

Thanks.

[StaceyKoprince]

I'll assume you understand why the two statements don't work individually, since you correctly discarded A, B and D as possibilities.

Statement 1 gives us one common point: (5,1)

Statement 2 tells us the y-intercept of n is greater than the y-intercept of p. The y-intercept is where a particular line crosses the y-axis. The corresponding point for that line is (0,y) with y representing the y-inntercept.

If n's y-intercept is greater than p's, then the value y is greater for n than for p. If you sketch a coordinate plane, place the point (5,1) on the plane, and then arbitrarily sketch some points along the y-axis:

1) try a pair above the y=1 line, with the higher labeled n and the lower labeled p. In this case, the two slopes are negative, and the slope of n is more negative than the slope of p. That is, n's slope is smaller than p's slope. Answer the question: Yes.
2) try a pair below the y=1 line, with the higher labeled n and the lower labeled p. In this case, the two slopes are positive, and the slope of n is closer to zero than the slope of p. That is, n's slope is smaller than p's slope. Answer the question: Yes.
3) you can also try some pairs where one or the other (n or p) has a y-intercept of 1. In each case, you'll continue to see that n's slope is always smaller than p's slope.

So, together, the statements are sufficient.

[victorgsiu]

Yes, you'll see that the lower (in number) the y-intercept, the larger the slope. Therefore, p's slope is always larger than n's slope.

[Ben Ku]

Victor's point is good, given that there is already a given point. In this case, it's (5,1).

[sudaif]

this is interesting, but i am now thoroughly confused.

i thought slope of a line is measured in terms of the change that occurs in y when x changes by a unit, or vice versa. if that is the correct definition of slope, then:

when both lines n and p have positive y-intercepts, then line n will be more steep coming down towards the intersection point (5,1). since it is more steep, thus its slope is greater.

can an instructor please help!?! I'm troubled by almost all line/slope questions and i thought i had it figured out till i read this post by Stacey. appreciate your help!

[RonPurewal]

this is interesting, but i am now thoroughly confused.

i thought slope of a line is measured in terms of the change that occurs in y when x changes by a unit, or vice versa. if that is the correct definition of slope, then:

when both lines n and p have positive y-intercepts, then line n will be more steep coming down towards the intersection point (5,1). since it is more steep, thus its slope is greater.

here's the problem -- you're not considering the sign of the slopes.

you're picturing two lines whose y-intercepts are both greater than 1.**
in this case, line n is steeper -- but, since both lines are sloping downward, this means that the slope of line n is a bigger negative number.
therefore, since the slope of p is a smaller negative number, it's "greater" than the slope of n.

e.g., -2 is greater than -4.

i get confused by this sort of thing all the time, too, but you've got to learn to keep it straight.

--

**i can tell this is what you were thinking, since you said that they're sloping "down" toward (5, 1).
note that this is not a justified assumption -- they could have a y-intercept at 1 (in which case they'd be horizontal), or a y-intercept less than 1 (in which case they would slope upward).

[sudaif]

Gotcha. Thanks Ron.

[tim]

:)

[juli.yeung]

Quick question:
If n's y-intercept is 3 and p's y-intercept is -2, the two slopes would be both |2|. BUT n has a -2 slope while p has a +2 slope, hence slope of n is less than slope of p. Is my logic correct? Thanks!

[mschwrtz]

right idea exactly juli, but not quite the right way to express it

by slope=|2|

you mean

|slope|=2

after all |2| is just 2

[aanchalsinha]

I know its been a while since this question has been discussed. But I would appreciate your response.

My solution went like this:

For line n eqn: y = ax + b
For line p eqn: y = cx + d

Question: a<c?

Statement 1 and 2 by themselves are insufficient.

St1: line n: 1 = 5a + b --> b=1-5a
line p: 1 = 5c + d --> d=1-5c

St2: b>d

St 1+2

1-5a > 1-5c --> SUFF ans C

Is my approach correct or is it just coincidence that the ans is C.

Thanks,
Aanchal

[RonPurewal]

aanchalsinha, yes, that works too.

[geeknick]

[deleted -- non gmat problem]

[RonPurewal]

geeknick, this is a forum for GMAT problems only. this is not a forum for homework help, or for other sorts of general math help.

please read the forum rules.
if you are here for GMAT help, welcome, and follow the rules when posting.
if you are not, sorry, please look elsewhere.

thanks.

[davidfrank]

Hi,

Need some clarification around this problem. Victor mentioned that the lower the y-intercept the steeper the line and hence a higher slope. If this is true then statement one is not needed.

Please clarify.