Question

The straight line $a x + b y + c = 0$, where $a b c \ne 0$, will pass through the first quadrant if

• A. $a c > 0, bc > 0$
• B. $c > 0$ and $bc < 0$
• C. $bc > 0$ and/or $ac > 0$
• D. $ac < 0$ and/or $bc < 0$

Answer 1

Answer: (D)

If the line meets the $x$- and $y$-axes at $A$ and $B$, then $A \equiv (-c/a , 0), B \equiv (0, -c/b )$. The line will pass through the first quadrant if
$-c/a > 0$ and/or $-c/b > 0$
i.e., $ac < 0$ and/or $bc < 0$