Question Find the slope of a line perpendicular to the line whose equation is $$ 3 x+18 y=108 $$. Fully simplify your answer.

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To find the slope of a line perpendicular to the given line $$ 3x + 18y = 108 $$, follow these steps:

### 1. Find the Slope of the Given Line

First, convert the equation $$ 3x + 18y = 108 $$ to **slope-intercept form** $$ y = mx + b $$, where $$ m $$ is the slope and $$ b $$ is the y-intercept.

$$
\begin{align*}
3x + 18y &= 108 \
18y &= -3x + 108 \quad &\text{(Subtract $$ 3x $$ from both sides)} \
y &= \frac{-3}{18}x + \frac{108}{18} \quad &\text{(Divide both sides by 18)} \
y &= -\frac{1}{6}x + 6
\end{align*}
$$

**Slope of the given line ($$ m $$):** $$ -\frac{1}{6} $$

### 2. Determine the Slope of the Perpendicular Line

Perpendicular lines have slopes that are **negative reciprocals** of each other. This means if one line has a slope of $$ m $$, the perpendicular line will have a slope of $$ -\frac{1}{m} $$.

$$
\text{Slope of perpendicular line} = -\frac{1}{m} = -\frac{1}{-\frac{1}{6}} = 6
$$

### **Final Answer**

The slope of a line perpendicular to $$ 3x + 18y = 108 $$ is **6**.
The slope of the perpendicular line is 6.

Question Find the slope of a line perpendicular to the line whose equation is \( 3 x+18 y=108 \). Fully simplify your answer.

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