To determine the slope of the line represented by the equation [tex]\( f(x) = -3x + 7 \)[/tex], we need to identify the coefficient of the [tex]\( x \)[/tex]-term.
The general form of a linear equation is [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] is the slope of the line,
- [tex]\( x \)[/tex] is the variable,
- [tex]\( b \)[/tex] is the y-intercept, the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
Now, comparing our given equation [tex]\( f(x) = -3x + 7 \)[/tex] with the general form [tex]\( y = mx + b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] (which corresponds to [tex]\( m \)[/tex] in the general form) is [tex]\( -3 \)[/tex].
Therefore, the slope of the line is [tex]\( -3 \)[/tex].
Hence, the correct answer is:
B. -3
