To solve this question, let's compare the slopes of the two given lines.
1. The equation of the first line is [tex]\(y = mx -4\)[/tex].
- The slope of this line is [tex]\(m\)[/tex].
2. The equation of the second line is [tex]\( y = x - 4\)[/tex].
- The slope of this line is [tex]\(1\)[/tex].
The problem states that the slope of the line [tex]\( y = mx - 4 \)[/tex] is less than the slope of the line [tex]\( y = x - 4 \)[/tex]. Therefore, we have the inequality:
[tex]\[ m < 1 \][/tex]
Thus, the correct condition is that [tex]\( m \)[/tex] must be less than [tex]\( 1 \)[/tex].
So, the answer is:
[tex]\[ m < 1 \][/tex]