Question

what is the slope of a line that is perpendicular to the line whose equation is $ax + by + c = 0$, $a\
eq0$ and $b\
eq0$? the slope of the line perpendicular to the line $ax + by + c = 0$ is \boxed{}.

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $Ax + By + C = 0$ to solve for $y$:
$$By = -Ax - C$$
$$y = -\frac{A}{B}x - \frac{C}{B}$$

Step2: Identify original slope

The slope of the given line is $m_1 = -\frac{A}{B}$.

Step3: Find perpendicular slope

Perpendicular slopes multiply to $-1$, so solve $m_1 \times m_2 = -1$:
$$-\frac{A}{B} \times m_2 = -1$$
$$m_2 = \frac{B}{A}$$

Answer:

$\frac{B}{A}$