If k and ℓ are lines in the xy-plane, is the slope of k less than the

Question

If k and l are lines in the xy-plane, is the slope of k less than the slope of l ?

(1) The x-intercept of line k is positive, and the x-intercept of line l is negative.
(2) Lines k and l intersect on the positive y-axis.

(DS13097)

KarishmaB · Accepted Answer

Relation between slope and intercepts of a line: Slope of a line = – (y intercept)/(x intercept) Is slopek < slopel ? Is - yk / xk < - yl / xl ? Is yk / xk > yl / xl ? (1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative. xk > 0 xl < 0 Since we don't know anything about yk and yl, this is not sufficient. (2) Lines k and ℓ intersect on the positive y-axis. This means both yk and yl are positive. But we don't know anything about xk and xl. Using both, yk/xk is positive because both yk and xk are positive. yl/xl is negative because yl is positive but xl is negative. Then, yk / xk is certainly greater than yl / xl. Sufficient. Answer (C)

Nikhil · Answer

To find if the slope of k less than the slope of ℓ

Statement 1

The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.

Case 1

K can have a +ve slope when k rises upward while running from left to right and ℓ can have a -ve slope when ℓ slides downward while running from left to right

=> slope of line k > slope of line ℓ

Case 2

K can have a -ve slope when k slides downwards while running from left to right and ℓ can have a +ve slope when ℓ rises upward while running from left to right

=> slope of line k < slope of line ℓ

Statement 1 is not sufficient

Statement 2

Lines k and ℓ intersect on the positive y-axis. Both the above mentioned cases are still possible

Statement 2 is not sufficient

Combining statements 1 and 2

Since x-intercept of line k is positive and y-intercept of line k is positive => K has negative slope

Since x-intercept of line ℓ is negative and y-intercept of line ℓ is positive => ℓ has positive slope

=> slope of line ℓ > slope of line k

Statements 1 and 2 together are sufficient

Hence option C

vikgupta07 · Answer

Equation: y=mx+c

Case 1 for line k: x intercept is -c/m>0
Case 1 for line l: x intercept is -c/m<0

Statement 1 is not Sufficient as in both the cases, either c could be -ve or m could be -ve

Case 2: Y intercept is positive => c is positive in the equation for both lines

Statement 2 is not Sufficient as in both the cases, slope information is not there

Combining

Case 1 for line k: x intercept is -c/m>0 , given c >0 , m is -ve
Case 1 for line l: x intercept is -c/m<0, given c>0, m is +ve

=> slope l>slope k or slope k<slope l - Sufficient

C

Hope this helps!

Salsanousi · Answer

Best way to solve it is to draw

Refer to the drawings to have an idea of how I solved it.

answer choice C

sayan640 · Answer

@Bunuel

@VeritasKarishma

@Chetan2u

If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?

(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.

Statement 1 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.

(2) Lines k and ℓ intersect on the positive y-axis.

Statement 2 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.

Combining it's sufficient as it leads to only one possibility i.e SLope of L is greater than slope of K.

Answer is option C.

I have attached three images in support of my explanation.

Please find them attached herewith.

Please Please give me kudos if you found my explanation helpful.

NEW question from GMAT® Quantitative Review 2019 
(DS13097)

sayan640 · Answer

Thanks 
 VeritasKarishma 
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?

Posted from my mobile device

KarishmaB · Answer

Sayan60,

Certainly there is nothing wrong with graphing out the question and I am a big proponent of making diagrams etc. Just that with multiple lines and slopes and various constraints given in the statements, I find it a bit confusing and worry about missing a case or two. So I have found that the slope and intercept method I discussed above is far more efficient in these cases.

Dpkkukreja · Answer

VeritasKarishma  can you please explain more about the slope formula that you used? All I knew was Slope= Rise/Run

KarishmaB · Answer

Check here: https://anaprep.com/geometry-using-slop ... fectively/

CEdward · Answer

Might be a silly question, but suppose you have two negative slopes and one of them is more negative than the other. Is it always the case that the more positive slope is larger? Or can the more negative one be 'steeper'? Maybe I got it twisted.

Bunuel · Answer

A steeper incline indicates a higher  absolute value  of the slope.

So, if both lines have positive slopes, then the line which is steeper has greater slope.
If both lines have negative slopes, then the line which is steeper has greater absolute value slope, its slope is "more negative", so less than the slope of another line.

760Abhi · Answer

Hello  KarishmaB  Ma'am,

Can we use the below formula anywhere or are there any constraints?

Slope of a line = – (y intercept)/(x intercept)

Thank you for your time.

KarishmaB · Answer

This is a generic formula for the slope of a line when the x intercept is not 0. Graph out a line and mark its y and x intercepts. The y and x intercepts give us two points on the line so the slope becomes defined. If the line passes through (0, 0), then both x and y intercepts are 0 and we get only one point and hence we cannot get the slope (mathematically, since x intercept is 0, we cannot use this expression)

gloomybison · Answer

Bunuel   KarishmaB 
what does "k and l intersect on positive y-axis" mean? 
is it that k's and l's y-intercept positive? or k's and l's intersection point has a positive y?

KarishmaB · Answer

It means that their point of intersection lies on the positive Y axis. 
So they intersect at a point such as (0, 3) or (0, 10) etc.

bumpbot · Answer

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If k and ℓ are lines in the xy-plane, is the slope of k less than the

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