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We are given the slope \( m = -9 \) and a point the line passes through: \( (-3, 1) \).

We need to write the equation in slope-intercept form: 
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Substitute the slope and the point into the equation.

The point-slope form of the line equation is:
\[
y - y_1 = m(x - x_1)
\]
Substituting \( m = -9 \), \( x_1 = -3 \), and \( y_1 = 1 \), we get:
\[
y - 1 = -9(x + 3)
\]

### Step 2: Simplify the equation.

Distribute the slope \( -9 \):
\[
y - 1 = -9x - 27
\]

Now, add 1 to both sides to isolate \( y \):
\[
y = -9x - 27 + 1
\]
\[
y = -9x - 26
\]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = -9x - 26
\]

Would you like a more detailed explanation or have any questions?

Here are five related questions to expand on this topic:
1. How do you find the equation of a line if you're given two points instead of a slope and a point?
2. What is the general formula for slope-intercept form?
3. How can you convert an equation in standard form to slope-intercept form?
4. What is the significance of the slope and y-intercept in the equation of a line?
5. Can the slope of a vertical line be represented in slope-intercept form?

**Tip**: Always check if you can simplify the equation further when working with fractions or decimal points.

Write the equation of the line with the given properties: Slope = -9, through (-3, 1).

Learn how to write the equation of a line given the slope (-9) and a point (-3, 1) in slope-intercept form. This detailed solution involves using the slope-intercept form and applying algebraic techniques. Suitable for students in Grades 8-10.

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