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The task is to write the equation of a line in slope-intercept form, given that the slope \( m = -1 \) and the line passes through the point \( (9, 4) \).

### Step 1: Slope-Intercept Form
The slope-intercept form of a line is:

\[
y = mx + b
\]

where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

### Step 2: Substitute the Slope
We are given that the slope \( m = -1 \). Substituting this into the equation:

\[
y = -x + b
\]

### Step 3: Solve for \( b \)
We can find the y-intercept \( b \) by using the point \( (9, 4) \). Substitute \( x = 9 \) and \( y = 4 \) into the equation:

\[
4 = -(9) + b
\]

\[
4 = -9 + b
\]

\[
b = 4 + 9 = 13
\]

### Step 4: Write the Final Equation
Now that we have \( b = 13 \), the equation of the line is:

\[
y = -x + 13
\]

This is the equation of the line in slope-intercept form.

Would you like any further explanation on this solution?

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Here are five questions that expand on this topic:
1. How do you determine the slope if you are given two points instead of one?
2. What is the significance of the y-intercept in a line's equation?
3. How do you convert slope-intercept form to standard form?
4. What happens to the equation if the line is vertical or horizontal?
5. How does the equation change if the slope is a fraction or zero?

**Tip:** When writing a line equation, always verify if the given point satisfies the final equation to avoid mistakes.

Write the equation of the line in slope-intercept form. It has a coefficient of m = -1 and passes through the point (9, 4).

Learn how to write the equation of a line in slope-intercept form with a slope of -1 that passes through the point (9, 4). This step-by-step guide explains the process using the slope formula and algebraic techniques. Suitable for students in Grades 7-9.

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