Question

find the slope of a line perpendicular to the line whose equation is $9x + 6y = 18$. fully simplify your answer.

Explanation:

Step1: Rewrite in slope-intercept form

Solve $9x + 6y = 18$ for $y$:

$$\begin{align*} 6y&=-9x + 18\\ y&=\frac{-9x + 18}{6}\\ y&=-\frac{3}{2}x + 3 \end{align*}$$

Step2: Identify original slope

The slope of the given line is $m_1 = -\frac{3}{2}$.

Step3: Find perpendicular slope

Perpendicular slopes are negative reciprocals: $m_2 = -\frac{1}{m_1}$

$$ m_2 = -\frac{1}{-\frac{3}{2}} = \frac{2}{3} $$

Answer:

$\frac{2}{3}$