Lines L and M intersect at (-2,-2). Is the Value of X- intercept of L

Edited the OA. Thank you for checking all the questions. Appreciate it.

P.S. You can tag only me in future posts. I'll take care of the edits.

Combined insufficient as shown in the graph below. The problem is if L has a positive slope, M can either have a smaller positive slope or negative slope which completely changes the x-intercept position.

I have a samll query
Stmt A:

If L is parallel to x axis its slope will be zero and if m is negative slope so l>m in slope but my qsn is if line is parallel to x axis so it has y intercept but no x intercept ,so how will this case fit in?or this is absolete case for such option

Given: Lines L and M intersect at (-2,-2).

Asked: Is the Value of X- intercept of L greater than that of M?

Let Line L be: y+2 = m1 (x+2) = m1x + 2m1; y = m1x + 2m1 -2 (1)
Let Line M be: y+2 = m2 (x+2) = m2x + 2m2; y = m2x + 2m2 -2 (2)

x - intercept of line L : y = 0 = m1x + 2m1 -2 ; x = 2(1-m1)/m1 = 2(1/m1 -1)
x - intercept of line M: y = 0 = m2x + 2m2 -2; x = 2(1-m2)/m2 = 2(1/m2 -1)

1) Slope of L is greater than that of M.
m1 > m2
Since signs of m1 & m2 are unknown
NOT SUFFICIENT

2) Slope of L is positive.
m1>0
Since there is no information about m2.
NOT SUFFICIENT

(1) + (2)
1) Slope of L is greater than that of M.
m1 > m2
Since signs of m1 & m2 are unknown
2) Slope of L is positive.
m1>0
Since sign of m2 is unknown
NOT SUFFICIENT

IMO E

Good question! This problem assumes L must have an x-intercept so we can ignore this special case. Besides that, this only fits in (1) which is insufficient anyways.

hi Kinshook

I am afraid the solution is wrong.

the operation here in statement 1
m1 > m2
1/m1<1/m2

assumes that m1 and m2 are positive .. which may not be the case.

lets say m1=1 and m2=-2, here m1>m2 but 1/m1>1/m2

statement 1 is therefore insufficient.

azhrhasan

Corrected. Thanks

Sorry this is my curiosity

Understood the M slope is the key here but what about the B - the y-intercept - in a way that even if the slope is the same - say is it correct to say that if the Y-intercept or the B is different, the X intercept also cant be determined?

I have some doubt in this question.
First, what is meaning of higher slope. With two negative values of m (y=mx+c), should we consider m with sign or without.
Second, should we consider x intercept with sign or not.
Please help .

Bunuel, please could you answer @sagerpgh question? I have a similar doubt. The question says "Is the Value of X- intercept of L greater than that of M?" Should we not consider sign here? If the x-intercept of a line is -2, would we take +2 or -2 to compare with the value of other slope? Thank you in advance!

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Hope it helps.

the answer should be A as in case when L has a positive slope and M has a negative slope, then the magintude of = X intercept of M is greater than that of L. So A should be sufficient . when we are talking about intercept , we only see magnitude not the sign of intercept . So i feel answer A should be correct