To determine the condition under which the slope of the line [tex]\( y = mx - 4 \)[/tex] is less than the slope of the line [tex]\( y = x - 4 \)[/tex], let's analyze the slopes of the given lines.
1. The slope of the line [tex]\( y = mx - 4 \)[/tex] is given directly by the coefficient of [tex]\( x \)[/tex], which is [tex]\( m \)[/tex].
2. The slope of the line [tex]\( y = x - 4 \)[/tex] is given directly by the coefficient of [tex]\( x \)[/tex], which is [tex]\( 1 \)[/tex].
We need to find under what condition the slope [tex]\( m \)[/tex] is less than the slope [tex]\( 1 \)[/tex].
Mathematically, we express this as:
[tex]\[ m < 1 \][/tex]
Thus, the condition that must be true about [tex]\( m \)[/tex] is:
[tex]\[ m < 1 \][/tex]
Considering the given options:
- [tex]\( m = -1 \)[/tex] does not generally apply, as it is a specific value.
- [tex]\( m = 1 \)[/tex] does not satisfy [tex]\( m < 1 \)[/tex].
- [tex]\( m < 1 \)[/tex] correctly reflects the required condition.
- [tex]\( m > 1 \)[/tex] does not satisfy [tex]\( m < 1 \)[/tex].
Therefore, the correct condition is:
[tex]\[ m < 1 \][/tex]
Given the options, the correct one is:
[tex]\[ m < 1 \][/tex]
This corresponds to the third option in the provided choices. The true must-be condition about [tex]\( m \)[/tex]:
[tex]\[ \boxed{m < 1} \][/tex]
In numerical terms, this corresponds to the index [tex]\( 2 \)[/tex] in the list of options. Hence, the numerical result is:
[tex]\[ 2 \][/tex]
