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

[RonPurewal]

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.

read the post directly under victor's.

[aliag916]

Hi, I'm still not sure why stmt 2 is not sufficient on its own. If the Y intercept of n is > than that of P, the slope of n is always < than slope of P.
If both the lines are going upwards: slope of n < slope p coz p will be steeper and Y/X will be greater than that of n's.
if both lines are going downwards: n has a greater negative slope than P. so slope of n < slope of p
if n goes down and p up: same result

Should I consider the case when n=1 so slope is 0 and p goes upwards. Then also slope of n < than slope of P

Any other point that I am missing?? ok so I missed parallel lines where the slopes would be equal. But if we were given that the lines p and n are not parallel would stmt 2 be sufficent?
Thank you!

[tim]

What you're not considering is the possibility that the lines could intersect somewhere where x is negative. In that situation, the slope of n is greater than that of p, whereas the opposite is true when the lines intersect to the right of the y-axis. Statement 1 helps then by letting us know on which side of the y-axis the lines intersect.

[aliag916]

Thanks, so if both the lines are below y=1, then also
the slope of n be > than slope P coz P would be the steeper line with a greater negative no and so a smaller slope? Pls do clarify if my thinking is correct or not

Thank u

[RonPurewal]

Thanks, so if both the lines are below y=1, then also
the slope of n be > than slope P coz P would be the steeper line with a greater negative no and so a smaller slope? Pls do clarify if my thinking is correct or not

Thank u

Please write this question out in complete sentences. Thanks.

[sasha.koslowsky]

Need to clarify one thing please:

In the stem it says "Is the slope of line n less than the slope of line p?", thus, it asks for the steepness of the slope and for example slope -5 would be steeper than slope 2, right? In other words a higher absolute value of a slope indicates a steeper incline, right?

If this is correct, a y-intercept of "2" (line n) and a y-intercept of "-21" (line p) would leed to a different solution, as line p would have a steeper slope than line n (also a higher absolute slope value).

Reference from the stem: (2) y-intercept n>p

Example 1:
n=2 -> slope = -1/5
p=-21 -> slope = 20/5 = 4

Result: slope p > slope n (steeper)

Example 2 with opposite result:
n=21 -> slope = -20/5 = -4
p=11 -> slope = -10/5 = -2

Result: slope n > slope p (steeper, absolute value)

So the solution would be E instead of C as it depends on where the two y-intercepts are placed on the y axis. Even if y-intercept of n>p it does not mean that slope of line n > slope of line p.... what I am doing wrong... help!!

Many thanks.

[RonPurewal]

Need to clarify one thing please:

In the stem it says "Is the slope of line n less than the slope of line p?", thus, it asks for the steepness of the slope and for example slope -5 would be steeper than slope 2, right? In other words a higher absolute value of a slope indicates a steeper incline, right?

It doesn't say "steeper incline". It is asking you whether one number is less than another number.

Example 2 with opposite result:
n=21 -> slope = -20/5 = -4
p=11 -> slope = -10/5 = -2

Result: slope n > slope p (steeper, absolute value)

-4 is less than -2.
Done.
That's it.

Don't invent complexity that's not actually there.

Much more importantly, NEVER try to dispute the official answers.
If you "disagree" with an official correct answer, then ... well, you're wrong.

[sasha.koslowsky]

Yeah, its the first question so far that I could not understand the solution. And you are right in Example two -4 is less than -2 (-4 is also steeper), but in Example 1 its the other way around.... Actually Example two is the common result that confirms the solution, and example one is the contradictory result that I found...

[sasha.koslowsky]

Ahhh, I think now I got it, both are less of course... jejeje... need some sleep I guess. Thanks!!!

[RonPurewal]

Sure.