Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 3, y, equals, 183x−3y=18. Fully simplify your answer.

We are given the equation of the line \(3x - 3y = 18\), and we need to find the slope of a line perpendicular to it.

### Step 1: Rewrite the equation in slope-intercept form (\(y = mx + b\)), where \(m\) is the slope.
We start with the given equation:

\[
3x - 3y = 18
\]

Solve for \(y\):

1. Subtract \(3x\) from both sides:
   \[
   -3y = -3x + 18
   \]
2. Divide the entire equation by \(-3\) to isolate \(y\):
   \[
   y = x - 6
   \]

The slope of the given line is the coefficient of \(x\), which is \(m = 1\).

### Step 2: Find the slope of the perpendicular line.
The slope of a line perpendicular to another is the negative reciprocal of the original slope. Since the slope of the original line is \(1\), the negative reciprocal of \(1\) is \(-1\).

Thus, the slope of the line perpendicular to the given line is:

\[
\boxed{-1}
\]

Would you like a deeper explanation, or have any questions?

Here are some related questions to expand your understanding:
1. What is the slope of a line parallel to \(3x - 3y = 18\)?
2. How do you convert an equation into slope-intercept form in general?
3. What is the geometric meaning of perpendicular slopes?
4. Can the slope of a line be zero, and what does that represent?
5. How do you find the slope of a vertical line?

**Tip:** The product of the slopes of two perpendicular lines is always \(-1\).

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

Learn how to find the slope of a line perpendicular to 3x - 3y = 18 by converting the equation to slope-intercept form and applying the concept of perpendicular slopes. This algebra problem is suitable for students in Grades 8-10 and covers key concepts like slope calculation and perpendicular lines.

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