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题库 / OG2017Q-DS-293
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.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
题目分析：
设直线k的斜率为a，直线ℓ的斜率为b，两条直线均过(1,1)点，所以，直线k的解析式为y=a(x-1)+1，截距为1-a。直线ℓ的解析式为y=b(x-1)+1，截距为1-b。题目要判断是否有1-a>1-b，即判断是否有b>a。
（1） 直线k的斜率a小于直线ℓ的斜率b，能够判断直线k的截距大于直线ℓ的截距。题目得解。
（2） 直线ℓ的斜率为正，无法得知直线k斜率和直线ℓ斜率的关系，也就无法判断截距的关系。不满足要求。
因此，本题答案为（A），仅条件1可以解题，条件2不行。
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