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To solve this, we need to find the equation of a line that is **perpendicular** to the line \( y - 7 = -x \) and passes through the point \( (9, 8) \).

### Step 1: Rewrite the given line in slope-intercept form.
The given equation is:
\[
y - 7 = -x
\]
Solving for \( y \), we get:
\[
y = -x + 7
\]
Thus, the slope of this line (\( m_1 \)) is \( -1 \).

### 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 given line is \( -1 \), the slope of the perpendicular line (\( m_2 \)) will be:
\[
m_2 = \frac{1}{-1} = 1
\]

### Step 3: Use the point-slope form of the equation.
Now that we know the slope of the perpendicular line is \( 1 \) and it passes through the point \( (9, 8) \), we can use the point-slope form of a line:
\[
y - y_1 = m(x - x_1)
\]
Substitute \( m = 1 \), \( x_1 = 9 \), and \( y_1 = 8 \):
\[
y - 8 = 1(x - 9)
\]
Simplify the equation:
\[
y - 8 = x - 9
\]
\[
y = x - 1
\]

### Final Answer:
The equation of the line that is perpendicular to \( y - 7 = -x \) and passes through the point \( (9, 8) \) is:
\[
y = x - 1
\]

Let me know if you would like further explanation or have any questions!

### Related Questions:
1. How do you find the equation of a line given two points?
2. What is the general method to find the slope of a perpendicular line?
3. How can you convert a line equation from standard form to slope-intercept form?
4. How does the point-slope form differ from slope-intercept form?
5. What happens when the slopes of two lines are the same?

### Tip:
For any line perpendicular to another, always remember the slopes must be negative reciprocals of each other (i.e., their product must equal \( -1 \)).

Find the equation of a line perpendicular to y - 7 = -x that passes through the point (9, 8).

Learn how to find the equation of a line that is perpendicular to y - 7 = -x and passes through the point (9, 8). This problem covers the slope-intercept form, point-slope form, and the negative reciprocal slope theorem, suitable for Grades 9-11.

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