Does the line with equation ax + by = c, where a, b and c are real con

We are given a line with equation ax+by = c, where a,b and c are real constants, and we need to determine whether it crosses the x-axis. Let’s start by isolating y in our given equation:

ax+by = c

by = -ax + c

y = (-a/b)x + (c/b)

We now have the given equation in slope-intercept form; the slope is -a/b and the y-intercept is c/b.

Statement One Alone:

b not equal to 0

Since we are not provided any information about the slope of the line, statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

ab>0

Since ab > 0, neither a nor b can be 0. This means that the slope of the line is not equal to zero. Recall that if the slope of a line is 0, the line is horizontal and will not cross the x-axis unless the line is the x-axis itself. Thus, regardless of the values of a or b, the line will, at some point, cross the x-axis.

Answer: B