Max@Math Revolution wrote:In the x-y plane, line K passes through (a,0) and (0,b). What is the slope of line K?
1) a/b=1
2) Line K passes through (1,2)

*An answer will be posted in 2 days.

(1) Sufficient. This implies a = b, and neither a, nor b, can equal zero. No matter what value of a and be are selected the resulting slope will be -1. This can be proven by the formula for slope: (y2-y1)/(x2-x1). Here, x1=a, x2=0, y1=0, and y2=b. If a=b, and a and b cannot equal zero, then let's set a=b=K where K is a new constant that represents the value of both a & b. So we have m = (K-0)/(0-K) = K/-K = -1.

(2) Not sufficient. We need at least two points to determine the slope. This could be on the line x=1 or the line y=2, or an infinite number of other lines.

Answer: A

If we modify the original condition and the question, the slope of a line that passes through (a,0) and (0,b) is (0-b)/(a-0)=-b/a. Thus, the correct answer is A.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.