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

To find the slope of a line perpendicular to the given line, we need to first determine the slope of the given line.

The equation of the line is:

\[
x - 3y = 27
\]

We can rewrite this equation in slope-intercept form, \( y = mx + b \), where \( m \) is the slope.

### Step 1: Solve for \( y \)
\[
x - 3y = 27
\]
Subtract \( x \) from both sides:
\[
-3y = -x + 27
\]
Now, divide by \(-3\) to isolate \( y \):
\[
y = \frac{1}{3}x - 9
\]

Here, the slope \( m \) of the given line is \( \frac{1}{3} \).

### Step 2: Find the slope of the perpendicular line
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. 

So, the negative reciprocal of \( \frac{1}{3} \) is:
\[
-\frac{1}{\frac{1}{3}} = -3
\]

### Final Answer:
The slope of the line perpendicular to the given line is \(\boxed{-3}\).

Would you like more details or have any other questions?

Here are some related questions to explore:

1. How do you find the slope of a line given two points?
2. What is the significance of the slope-intercept form of a line?
3. How can you determine if two lines are parallel?
4. What does it mean for two lines to be perpendicular in terms of their slopes?
5. How do you graph a line given its slope and y-intercept?

**Tip:** Remember that the slope of a line is a measure of its steepness. Perpendicular lines have slopes that multiply to \(-1\).

Learn how to find the slope of a line perpendicular to x - 3y = 27 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations, slopes, and perpendicular lines. Suitable for students in Grades 7-9.

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