Find the slope of a line parallel to the line whose equation is \( 10 x+12 y=-120 \). Fully simplify your answer.

To find the slope of a line parallel to the given line, we first need to determine the slope of the line represented by the equation \( 10x + 12y = -120 \). 1. **Rearranging the equation into slope-intercept form (y = mx + b)**: - Start with the original equation: \[ 10x + 12y = -120 \] - Isolate \( y \) by moving \( 10x \) to the other side: \[ 12y = -10x - 120 \] - Divide every term by \( 12 \) to solve for \( y \): \[ y = -\frac{10}{12}x - 10 \] 2. **Simplifying the slope**: - The slope \( m \) is the coefficient of \( x \), which is \( -\frac{10}{12} \). - Simplifying \( -\frac{10}{12} \): \[ -\frac{10}{12} = -\frac{5}{6} \] 3. **Finding the slope of the parallel line**: - Lines that are parallel have the same slope. Therefore, the slope of the line parallel to the given line is also \( -\frac{5}{6} \). Thus, the slope of a line parallel to the line whose equation is \( 10x + 12y = -120 \) is \( \boxed{-\frac{5}{6}} \).