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The problem requires finding the slope, x-intercept, and y-intercept for the line given by the equation:

\[
-9x - 3y - 16 = 0
\]

Let's solve this step-by-step.

### Step 1: Rewrite the Equation in Slope-Intercept Form
To find the slope, we'll first convert this equation to the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. Start with:
   \[
   -9x - 3y - 16 = 0
   \]

2. Rearrange the equation to solve for \( y \):
   \[
   -3y = 9x + 16
   \]

3. Divide every term by \(-3\):
   \[
   y = -3x - \frac{16}{3}
   \]

Now, we have the equation in the form \( y = mx + b \) with:
- **Slope** (\( m \)) = \(-3\)
- **Y-intercept** (\( b \)) = \(-\frac{16}{3}\)

In decimal form:
- Slope = \(-3\)
- Y-intercept = \(-5.33\)

### Step 2: Find the X-intercept
To find the x-intercept, set \( y = 0 \) and solve for \( x \):

1. Substitute \( y = 0 \) in the original equation:
   \[
   -9x - 3(0) - 16 = 0
   \]
   \[
   -9x - 16 = 0
   \]

2. Solve for \( x \):
   \[
   -9x = 16
   \]
   \[
   x = -\frac{16}{9}
   \]

In decimal form, the x-intercept is approximately:
- X-intercept = \(-1.78\)

### Summary of Results
- **Slope** = \(-3\)
- **X-intercept** = \(-1.78\)
- **Y-intercept** = \(-5.33\)

Would you like further details on any part of this solution?

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Here are 5 related questions for practice:
1. How do you find the slope of a line if given two points?
2. What is the process to convert a line equation from general form to slope-intercept form?
3. How can you determine if two lines are parallel based on their slopes?
4. How do you calculate the distance between two points on a line?
5. What does the y-intercept represent in a real-world context?

**Tip:** When converting to decimals, always check for rounding accuracy, especially in intermediate steps!

Find the slope, x-intercept, and y-intercept for the line -9x - 3y - 16 = 0.

This problem guides you through finding the slope, x-intercept, and y-intercept for the line -9x - 3y - 16 = 0. Learn to rewrite the equation in slope-intercept form, identify the slope, and calculate intercepts. Ideal for students in Grades 9-10.

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