NOTE: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.In the xy-plane, what is the y-intercept of line l?
1) the slope of line l is 3 times its y-intercept
2) the x-intercept of line l is -(1/3)
Target question: What is the y-intercept of line L?
IMPORTANT: If the x-intercept is -1/3 (as per statement 2), the slope of the line is GUARANTEED to be 3 times its y-intercept (as per statement 1).
Here's why...
From statement 2, we know that (-1/3, 0) is one point on the line. Let's let (0, k) be the coordinates of the y-intercept of the line. In other words, let's let the y-intercept equal k.
Using the slope formula, the slope = (k - 0)/(0 - (-1/3)) = k/(1/3) = 3k
So, if the y-intercept is k, the slope must be 3k.
In other words, statement 1 provides no new information beyond the information that statement 1 provides. So, if statement 2 is sufficient, then statement 1 must also be sufficient (since it provides no new info). Conversely, if statement 2 is NOT sufficient, then statement 1 is NOT sufficient. At this point, we know that the answer must be either D (they're both sufficient) or E (neither is sufficient).
So, which is it?
Well, if we examine statement 2 on its own (the x-intercept is -1/3), we can see that we do not have enough information to determine the y-intercept of line L.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Since statement 1 provides no additional information, it too is NOT SUFFICIENT.
So, the combined statements are NOT SUFFICIENT
Answer = E
For additional proof, consider these two lines:
Both lines satisfy the conditions in statements 1 and 2, however the y-intercepts are different.
Cheers,
Brent
