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To find the slope of a line parallel to the line given by the equation:

\[
2x + 12y = -192
\]

we first need to rewrite this equation in slope-intercept form, \( y = mx + b \), where \( m \) represents the slope.

### Step 1: Isolate \( y \)

Starting with:
\[
2x + 12y = -192
\]

1. Subtract \( 2x \) from both sides:
   \[
   12y = -2x - 192
   \]

2. Divide every term by 12 to solve for \( y \):
   \[
   y = -\frac{2}{12}x - \frac{192}{12}
   \]

3. Simplify the fractions:
   \[
   y = -\frac{1}{6}x - 16
   \]

### Step 2: Identify the Slope

Now that the equation is in slope-intercept form, we can see that the slope \( m \) is \( -\frac{1}{6} \).

### Answer

Since parallel lines have the same slope, the slope of a line parallel to this one is also:
\[
-\frac{1}{6}
\]

Would you like more details or have any questions?

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Here are five related questions to deepen understanding:

1. How would you find the slope of a line perpendicular to this one?
2. What are the general steps for converting any linear equation to slope-intercept form?
3. How can we determine if two lines are parallel just by looking at their equations?
4. What is the significance of the y-intercept in the context of slope-intercept form?
5. How does the slope affect the angle of the line with respect to the x-axis?

**Tip:** For parallel lines, remember that their slopes are identical, while perpendicular lines have slopes that are negative reciprocals.

Find the slope of a line parallel to the line whose equation is 2x + 12y = -192. Fully simplify your answer.

Learn how to find the slope of a line parallel to the equation 2x + 12y = -192. This problem covers concepts such as slope, parallel lines, and converting to slope-intercept form. Suitable for students in Grades 8-10.

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