To determine the correct answer for the given question, we need to compare the slopes of the two lines provided in the equations [tex]\( y = mx - 4 \)[/tex] and [tex]\( y = x - 4 \)[/tex].
1. Identify the slopes of each line:
- The general form of a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope of the line.
- For the line [tex]\( y = mx - 4 \)[/tex], the slope is [tex]\( m \)[/tex].
- For the line [tex]\( y = x - 4 \)[/tex], the slope is 1.
2. Comparing the slopes:
- The problem states that the slope of the line [tex]\( y = mx - 4 \)[/tex] must be less than the slope of the line [tex]\( y = x - 4 \)[/tex].
- Therefore, we need [tex]\( m \)[/tex] to be less than 1.
Mathematically, this inequality can be expressed as:
[tex]\[
m < 1
\][/tex]
3. Analyze each option:
- [tex]\( m = -1 \)[/tex]: This value indeed satisfies [tex]\( m < 1 \)[/tex].
- [tex]\( m = 1 \)[/tex]: This value does NOT satisfy [tex]\( m < 1 \)[/tex] because [tex]\( 1 \)[/tex] is not less than [tex]\( 1 \)[/tex].
- [tex]\( m < 1 \)[/tex]: This is directly the inequality that we need.
- [tex]\( m > 1 \)[/tex]: This value does NOT satisfy [tex]\( m < 1 \)[/tex].
Given our analysis:
The correct option is:
[tex]\[
\boxed{m < 1}
\][/tex]
