To determine the slope of the line given by the equation [tex]\( y = -3x \)[/tex], we need to consider the general form of a linear equation, which is:
[tex]\[ y = mx + b \][/tex]
In this equation:
- [tex]\( m \)[/tex] represents the slope of the line
- [tex]\( b \)[/tex] represents the y-intercept, the point where the line crosses the y-axis
Comparing the given equation [tex]\( y = -3x \)[/tex] with the general form [tex]\( y = mx + b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] in [tex]\( y = -3x \)[/tex] is [tex]\(-3\)[/tex].
- There is no constant term added, so essentially [tex]\( b = 0 \)[/tex].
Thus, in the given equation [tex]\( y = -3x \)[/tex], we can see that the slope [tex]\( m \)[/tex] is [tex]\(-3\)[/tex].
Therefore, the slope of the line is:
[tex]\[ \boxed{-3} \][/tex]
