Find the slope of a line perpendicular to the line whose equation is x, plus, y, equals, x+y=9. Fully simplify

To find the slope of a line perpendicular to the given line \(x + y = 9\), we first need to determine the slope of the line represented by this equation.

### Step 1: Rearrange the equation into slope-intercept form
The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope.

Starting with the equation:
\[
x + y = 9
\]

Subtract \(x\) from both sides to solve for \(y\):
\[
y = -x + 9
\]

Now the equation is in the form \(y = mx + b\), where \(m = -1\).

### 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. Since the slope of the original line is \(-1\), the negative reciprocal is:

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

### Final Answer:
The slope of the line perpendicular to \(x + y = 9\) is \(1\).

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Would you like more details or further explanation? Here are 5 related questions to explore this concept:

1. How do you find the slope of a line from two points?
2. What is the slope of a line parallel to \(x + y = 9\)?
3. What happens to the equation of the line if the slope changes but the intercept remains the same?
4. Can a vertical line have a slope?
5. How do we apply the concept of perpendicular slopes in coordinate geometry?

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

Find the slope of a line perpendicular to the line whose equation is x + y = 9. Fully simplify.

Learn how to find the slope of a line perpendicular to x + y = 9 in this detailed, step-by-step solution. This problem covers core algebraic concepts, such as linear equations and perpendicular slopes, and is suitable for students in Grades 8-10.

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