To determine the slope of the line given by the equation [tex]\( y = -3x \)[/tex], we should recognize that this equation is in the slope-intercept form, [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( c \)[/tex] represents the y-intercept.
In the given equation [tex]\( y = -3x \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is [tex]\(-3\)[/tex].
- There is no constant term [tex]\( c \)[/tex], which means [tex]\( c = 0 \)[/tex].
From the slope-intercept form ( [tex]\( y = mx + c \)[/tex] ), we can identify the slope [tex]\( m \)[/tex] directly as the coefficient of [tex]\( x \)[/tex]. Here, the coefficient of [tex]\( x \)[/tex] is [tex]\(-3\)[/tex].
Therefore, the slope of the line is [tex]\(-3\)[/tex].
Among the given options:
A. [tex]\( 3 \)[/tex]
B. [tex]\(-3\)[/tex]
C. [tex]\(\frac{1}{3}\)[/tex]
D. [tex]\(-\frac{1}{3}\)[/tex]
The correct answer is B. [tex]\(-3\)[/tex].
