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To find the equation of a line in the form \( Ax + By = C \), given that the line passes through the point \( (-3, -9) \) and has a slope of \( -2 \), we can use the point-slope form of the equation of a line and then convert it to the desired form.

### Step 1: Use the Point-Slope Form
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is the point on the line. Substituting the given slope \( m = -2 \) and the point \( (-3, -9) \):

\[
y - (-9) = -2(x - (-3))
\]
\[
y + 9 = -2(x + 3)
\]

### Step 2: Simplify the Equation
Now distribute the slope on the right-hand side:
\[
y + 9 = -2x - 6
\]
Subtract 9 from both sides:
\[
y = -2x - 6 - 9
\]
\[
y = -2x - 15
\]

### Step 3: Convert to Standard Form \( Ax + By = C \)
To convert this into \( Ax + By = C \), we need to move all the terms to one side:
\[
2x + y = -15
\]

Thus, the equation in the form \( Ax + By = C \) is:
\[
2x + y = -15
\]

This is the desired equation. 

Would you like further clarification on any step?

Here are some related questions to extend your understanding:
1. How would the equation change if the slope were positive instead of negative?
2. What happens if the line passes through a different point but has the same slope?
3. How can you find the slope of a line if you're given two points instead of one point and the slope?
4. What is the geometric interpretation of the constants \( A \), \( B \), and \( C \) in the standard form \( Ax + By = C \)?
5. How can you graph a line using its equation in standard form?

**Tip:** To easily convert between different forms of line equations, always keep the slope-intercept form in mind, as it's the most intuitive for visualizing lines.

A line passes through point (-3, -9) and has a slope of -2. Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.

Learn how to write the equation of a line passing through point (-3, -9) with slope -2. Convert the equation into standard form Ax + By = C, following step-by-step explanations. Suitable for high school students in Grades 9-12.

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