BTGModeratorVI wrote: ↑Thu Dec 03, 2020 2:44 pm
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
