Question

find the slope of a line perpendicular to the line whose equation is 3x - 6y = 90. fully simplify your answer.

Explanation:

Step1: Rewrite in slope - intercept form

First, rewrite $3x - 6y=90$ as $y = mx + b$.
$3x-6y = 90$ can be rewritten as $-6y=-3x + 90$. Then $y=\frac{1}{2}x - 15$. The slope of this line $m_1=\frac{1}{2}$.

Step2: Use perpendicular slope formula

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 $m_1=\frac{1}{2}$, then $\frac{1}{2}\times m_2=-1$. Solving for $m_2$ gives $m_2=-2$.

Answer:

$-2$