Question

find the slope of a line perpendicular to the line whose equation is $9x + 3y = 36$. fully simplify your answer.

Explanation:

Step1: Rewrite in slope-intercept form

Rearrange $9x + 3y = 36$ to $y=mx+b$:
$$3y = -9x + 36$$
$$y = -3x + 12$$

Step2: Identify original slope

The slope $m_1$ of the given line is $-3$.

Step3: Find perpendicular slope

Perpendicular slopes are negative reciprocals:
$$m_2 = -\frac{1}{m_1} = -\frac{1}{-3} = \frac{1}{3}$$

Answer:

$\frac{1}{3}$