In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

[BTGModeratorVI]

In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.

Answer: A
Source: official guide

[Brent@GMATPrepNow]

In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.

Answer: A
Source: official guide

Given: In the xy-plane, lines k and l intersect at the point (1,1).

Target question: Is the y-intercept of k greater than the y-intercept of l?

Statement 1: The slope of k is less than the slope of l.
Let's examine 2 cases, and then make a generalization.

CASE A) the slope of line k is POSITIVE
For example, let's say line k has slope 1.

If line l has a greater slope (like a slope of 2), we can see that the y-intercept of k IS greater than the y-intercept of l
We can further see that if line l has a slope of 3, 4, 5, 6 etc , it will always be the case that the y-intercept of k IS greater than the y-intercept of l

CASE B) the slope of line k is NEGATIVE
For example, let's say line k has slope -1.5

If line l has a greater slope (like a slope of -0.6), we can see that the y-intercept of k IS greater than the y-intercept of l
We can further see that if line l has a slope that's greater than line k, it will always be the case that the y-intercept of k IS greater than the y-intercept of l

In both of the above cases, the answer to the target question will be the y-intercept of k IS greater than the y-intercept of l 00
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The slope of l is positive.
No information about line k
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

[swerve]

In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.

Answer: A
Source: official guide

First line equation \(1= m+c\), second line equation \(1 = n+b\), question asks whether \(c > b\)

From the two equations above,

\(c = 1-m\), \(b = 1-n\), therefore we need a relation between the \(2\) slopes to solve

From the first, \(m > n\) this \((1-m) < ( 1-n)\) and therefore \(b > c\). Sufficient \(\Large{\color{green}\checkmark}\)

From the second, we have only one slope and no relation between the \(2\) slopes. Not Sufficient \(\Large{\color{red}\chi}\)

Therefore, A