Slope of 3*x*−12*y*=−108. Fully simplify your answer.

To find the slope of the equation \( 3x - 12y = -108 \), we need to rewrite it in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.

### Step-by-step solution:
1. Start with the given equation:
   \[
   3x - 12y = -108
   \]

2. Isolate the term with \( y \). Subtract \( 3x \) from both sides:
   \[
   -12y = -3x - 108
   \]

3. Divide the entire equation by \( -12 \) to solve for \( y \):
   \[
   y = \frac{-3x - 108}{-12}
   \]

4. Simplify both terms:
   \[
   y = \frac{-3}{-12}x + \frac{-108}{-12}
   \]
   \[
   y = \frac{1}{4}x + 9
   \]

Now the equation is in slope-intercept form \( y = \frac{1}{4}x + 9 \), where the slope \( m = \frac{1}{4} \).

### Final Answer:
The slope of the equation is \( \frac{1}{4} \).

Would you like a detailed breakdown of any step? Here are 5 related questions to further explore:

1. What is the significance of the slope in a linear equation?
2. How do you interpret a negative slope in real-world situations?
3. How do you convert an equation from standard form to slope-intercept form?
4. What is the y-intercept in this equation, and how does it affect the graph?
5. How do you find the slope between two points on a line?

**Tip:** When simplifying fractions, always check if both the numerator and denominator have common factors for easier reduction.

Learn how to find the slope of the linear equation 3x - 12y = -108 by converting it into slope-intercept form. This detailed step-by-step solution explains how to isolate y and simplify terms. Suitable for students in Grades 8-10.

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