The question is asking if this particular line crosses the x-axis. Try thinking about the opposite: the only lines that will never cross the x-axis are horizontal lines. Horizontal lines have a slope of 0.Does the line with the equation ax + by = c, where a, b, cand c are real constants, cross the x-axis?
(1) b ≠0
(2) ab > 0
Rephrased question: does the line have a non-zero slope?
First, rearrange the the equation into y = mx + b form:
y = (-ax)/b + c/b
Thus, the slope = -a/b
The only way for this slope to be 0 is is a = 0. So rephrase again:
Further rephrased question: Does the variable a represent a non-zero number?
(1) b ≠0
This tells us nothing about a. Insufficient.
(2) ab > 0
If the product of a and b is greater than 0, then a ≠0. Sufficient!
The answer is B.
