To determine the values of [tex]\( m \)[/tex] for which the slope of the line [tex]\( y = mx - 4 \)[/tex] is less than the slope of the line [tex]\( y = x - 4 \)[/tex], we first need to understand the slopes of both lines.
1. Identify the slopes:
- The equation of the first line is [tex]\( y = mx - 4 \)[/tex]. The slope of this line is [tex]\( m \)[/tex].
- The equation of the second line is [tex]\( y = x - 4 \)[/tex]. The slope of this line is [tex]\( 1 \)[/tex].
2. Set up the inequality:
We need the slope of the first line to be less than the slope of the second line. Mathematically, this is:
[tex]\[
m < 1
\][/tex]
3. Analyze the given options:
- [tex]\( m = -1 \)[/tex]: This satisfies [tex]\( m < 1 \)[/tex].
- [tex]\( m = 1 \)[/tex]: This does not satisfy [tex]\( m < 1 \)[/tex] because it results in equality, not the desired inequality.
- [tex]\( m < 1 \)[/tex]: This directly aligns with the condition that [tex]\( m \)[/tex] must be less than 1.
- [tex]\( m > 1 \)[/tex]: This does not satisfy [tex]\( m < 1 \)[/tex].
Therefore, the condition that must be true about [tex]\( m \)[/tex] is [tex]\( m < 1 \)[/tex]. The correct answer is:
[tex]\[ m < 1 \][/tex]
