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

The equation of the line given is:

\[
3x - 3y = 18
\]

To find the slope of a line perpendicular to this line, we need to first express the given line in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope.

### Step 1: Simplify the Equation
We start by simplifying the equation:

\[
3x - 3y = 18
\]

Divide the entire equation by 3:

\[
x - y = 6
\]

Now, solve for \(y\):

\[
y = x - 6
\]

So, the equation in slope-intercept form is:

\[
y = 1x - 6
\]

Here, the slope \(m\) of the line is \(1\).

### Step 2: Find the Perpendicular Slope
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the original line. The slope of the original line is \(1\), so the slope of the perpendicular line is:

\[
m_{\text{perpendicular}} = -\frac{1}{1} = -1
\]

Thus, the slope of the line perpendicular to the given line is \(-1\).

Would you like any further details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. How do you find the slope of a line from two points?
2. What is the slope-intercept form of a line?
3. How do you determine if two lines are parallel or perpendicular?
4. What is the equation of a line that passes through a specific point and has a given slope?
5. How does the slope of a line relate to its steepness?

**Tip:** When dealing with perpendicular slopes, remember that their product is always \(-1\).

Learn how to find the slope of a line perpendicular to the equation 3x - 3y = 18. This problem involves linear equations and the concept of perpendicular slopes. Suitable for high school students in Grades 9-12.

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