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Let’s solve the problem!

The task is to write the equation of a line in **slope-intercept form** (\(y = mx + b\)). We're given:

- **Slope** \(m = -9\)  
- A point on the line \((3, -6)\)

### Step 1: Plug into the slope-intercept form

We know:
\[
y = mx + b
\]
Using the point \((x, y) = (3, -6)\) and \(m = -9\), we substitute these into the equation to solve for \(b\) (the y-intercept).

\[
-6 = -9(3) + b
\]

\[
-6 = -27 + b
\]

\[
b = -6 + 27 = 21
\]

### Step 2: Write the final equation

Now that we know the slope is \(-9\) and the y-intercept \(b\) is \(21\), the equation of the line is:

\[
y = -9x + 21
\]

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The equation in **slope-intercept form** is:
\[
y = -9x + 21
\]

Do you have any questions, or would you like a deeper explanation? 

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Here are 5 related questions for further practice:
1. How do you convert an equation in standard form to slope-intercept form?
2. What is the significance of the slope in real-world applications?
3. How can you find the equation of a line given two points?
4. What happens to the graph if the slope is positive instead of negative?
5. How do parallel and perpendicular lines relate in terms of their slopes?

**Tip:** Always double-check your algebra when solving for the y-intercept to avoid small calculation errors.

Write the equation of a line in slope-intercept form given the slope is -9 and the line passes through the point (3, -6).

Learn how to write the equation of a line in slope-intercept form when given a slope of -9 and a point (3, -6). This detailed explanation walks through the steps to solve for the y-intercept and provides the final equation. Suitable for students in Grades 8-10.

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