To solve the problem, let's break it down step by step:

Given:

The equation of the line is: $x - 3y = 27$

Step 1: Rewrite the equation in slope-intercept form $y = mx + b$

We start by solving for $y$:

$x - 3y = 27$ $-3y = -x + 27$ $y = \frac{1}{3}x - 9$

Here, the slope $m$ of the line is $\frac{1}{3}$.

Step 2: Determine the slope of the line perpendicular to the given line.

The slope of a line perpendicular to another line is the negative reciprocal of the original slope.

Since the slope $m$ of the original line is $\frac{1}{3}$, the slope of the perpendicular line will be: $m_{\text{perpendicular}} = -\frac{1}{\frac{1}{3}} = -3$

Final Answer:

The slope of the line perpendicular to the given line is $-3$.

Would you like more details or have any other questions?

Here are 5 related questions to consider:

1. How do you find the slope of a line given two points on the line?
2. What is the significance of the slope-intercept form of a linear equation?
3. How would you find the equation of a line perpendicular to another line passing through a specific point?
4. How does the concept of negative reciprocals apply to parallel lines?
5. How can the distance between a point and a line be calculated?

Tip: Always remember that the slopes of perpendicular lines are negative reciprocals of each other.