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The problem asks for the equation of a line that passes through the point \((-1, -4)\) and has a slope of 9, expressed in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers.

### Step-by-Step Solution:

1. **Point-Slope Form**: We can start by using the point-slope form of a line:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \(m\) is the slope and \((x_1, y_1)\) is the point on the line. Here, \(m = 9\), \(x_1 = -1\), and \(y_1 = -4\).

   Substituting these values, we get:
   \[
   y - (-4) = 9(x - (-1))
   \]
   Simplifying:
   \[
   y + 4 = 9(x + 1)
   \]
   \[
   y + 4 = 9x + 9
   \]

2. **Rearranging into Slope-Intercept Form**:
   \[
   y = 9x + 9 - 4
   \]
   \[
   y = 9x + 5
   \]
   This is the slope-intercept form of the line.

3. **Converting to Standard Form**: Now we convert it to the form \(Ax + By = C\). We need to move all terms to one side of the equation:
   \[
   9x - y = -5
   \]
   This is the equation in the required form, where \(A = 9\), \(B = -1\), and \(C = -5\).

### Final Answer:
\[
9x - y = -5
\]

Would you like more details on any part of the process or have further questions?

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Here are five related questions:
1. How do you convert any line equation from slope-intercept form to standard form?
2. What is the general form of a line equation, and how does it differ from the slope-intercept form?
3. How would the equation change if the slope were negative or a fraction?
4. Can you find the equation of a line parallel to this one but passing through a different point?
5. How would you find the distance between this line and a given point not on the line?

**Tip**: When converting from slope-intercept form to standard form, always aim to keep \(A\), \(B\), and \(C\) as integers and \(A\) positive.

A line passes through point (-1, -4) and has a slope of 9. Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.

Learn how to find the equation of a line passing through the point (-1, -4) with a slope of 9. This solution uses the point-slope form and converts it into the standard form Ax + By = C, suitable for students in Grades 8-10.

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