To determine the slope of a line that is parallel to the line given by the equation [tex]\( y = -\frac{1}{3}x - 15 \)[/tex], we first need to understand the concept of parallel lines. Parallel lines have the same slope.
The given equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
For the equation [tex]\( y = -\frac{1}{3}x - 15 \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\(-\frac{1}{3} \)[/tex].
Therefore, any line that is parallel to this line will have the same slope.
Thus, the slope of a line that is parallel to [tex]\( y = -\frac{1}{3}x - 15 \)[/tex] is [tex]\(-\frac{1}{3}\)[/tex].
The correct answer is [tex]\(-\frac{1}{3}\)[/tex].
