To solve this problem, let's start by understanding the slopes of the given lines.
1. Identify the slope of the line [tex]\( y = mx - 4 \)[/tex]:
- A line in the form [tex]\( y = mx + b \)[/tex] has a slope [tex]\( m \)[/tex].
- Thus, the slope of the line [tex]\( y = mx - 4 \)[/tex] is [tex]\( m \)[/tex].
2. Identify the slope of the line [tex]\( y = x - 4 \)[/tex]:
- Again, a line in the form [tex]\( y = mx + b \)[/tex] has a slope [tex]\( m \)[/tex].
- Here, [tex]\( y = x - 4 \)[/tex] can be written as [tex]\( y = 1 \cdot x - 4 \)[/tex].
- Therefore, the slope of this line is [tex]\( 1 \)[/tex].
3. Compare the slopes of the two lines:
- We need 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].
- Mathematically, this is: [tex]\( m < 1 \)[/tex].
Thus, the correct answer is:
[tex]\[ m < 1 \][/tex]
So, the condition that must be true about [tex]\( m \)[/tex] is [tex]\( m < 1 \)[/tex]. The corresponding choice is:
[tex]\[
m < 1
\][/tex]
