Question

question
find the slope of a line perpendicular to the line whose equation is 3x + 6y = -54. fully simplify your answer.

Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope. We start with the equation $3x+6y=-54$.
Subtract $3x$ from both sides: $6y=-3x - 54$.
Then divide each term by 6: $y=\frac{-3x}{6}-\frac{54}{6}$, which simplifies to $y =-\frac{1}{2}x-9$.
So the slope of the given line, $m_1$, is $-\frac{1}{2}$.

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_2$. Then we have the equation $m_1\times m_2=-1$.
We know that $m_1 =-\frac{1}{2}$, so substitute it into the equation: $-\frac{1}{2}\times m_2=-1$.
To solve for $m_2$, multiply both sides of the equation by - 2: $m_2=(-1)\times(-2) = 2$.

Answer:

2