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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?

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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.

Find the slope of a line perpendicular to the line whose equation is x - 3y = 27. Fully simplify your answer.

Learn how to find the slope of a line perpendicular to the line whose equation is x - 3y = 27. This problem demonstrates key algebraic concepts, including the use of the slope-intercept form and understanding the relationship between the slopes of perpendicular lines. Suitable for students in Grades 8-10.

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