Question

question find the slope of a line perpendicular to the line whose equation is 6x - 9y = 216. fully simplify your answer.

Explanation:

Step1: Rewrite the given line in slope - intercept form

First, rewrite $6x - 9y=216$ in $y = mx + b$ form.
$6x-9y = 216$ can be rewritten as $-9y=-6x + 216$. Then $y=\frac{6}{9}x-24=\frac{2}{3}x - 24$. The slope of this line $m_1=\frac{2}{3}$.

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. Let the slope of the perpendicular line be $m_2$.
Since $m_1=\frac{2}{3}$, then $\frac{2}{3}m_2=-1$. Solving for $m_2$, we get $m_2=-\frac{3}{2}$.

Answer:

$-\frac{3}{2}$