Find the slope of a line parallel to the line whose equation is 10, x, plus, 12, y, equals, minus, 12010*x*+12*y*=−120. Fully simplify your answer.

To find the slope of a line parallel to the given line with the equation

\[
10x + 12y = -120,
\]

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

### Step-by-step Solution

1. **Rewrite the equation to solve for \(y\):**

   Start with the given equation:

   \[
   10x + 12y = -120.
   \]

   Subtract \(10x\) from both sides to isolate the term with \(y\) on the left:

   \[
   12y = -10x - 120.
   \]

2. **Divide every term by 12 to solve for \(y\):**

   \[
   y = \frac{-10x - 120}{12}.
   \]

   Simplify the right side by dividing each term separately by 12:

   \[
   y = \frac{-10}{12}x + \frac{-120}{12}.
   \]

   Simplify the fractions:

   \[
   y = -\frac{5}{6}x - 10.
   \]

   Now, the equation is in slope-intercept form, \(y = mx + b\), where \(m = -\frac{5}{6}\).

3. **Identify the slope:**

   The slope \(m\) of the given line is \(-\frac{5}{6}\).

4. **Find the slope of a parallel line:**

   Lines that are parallel have the **same slope**. Therefore, the slope of a line parallel to the given line is also:

\[
\boxed{-\frac{5}{6}}.
\]

Would you like more details on any step, or do you have any questions?

Here are some related questions:

1. How do you find the slope of a line given two points on the line?
2. What is the slope of a line perpendicular to the given line?
3. How do you graph a line given its slope and y-intercept?
4. How can you determine if two lines are parallel or perpendicular?
5. How does the slope affect the steepness and direction of a line?

**Tip:** When finding the slope of parallel lines, remember that they will always have the same slope.

Learn how to find the slope of a line parallel to the equation 10x + 12y = -120. Step-by-step solution provided, simplifying the process to find the slope of parallel lines. Suitable for high school students studying algebra and linear equations.

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