To determine the relationship between [tex]\( m \)[/tex] in the equation [tex]\( y = m x - 4 \)[/tex] and the slope of the line [tex]\( y = x - 4 \)[/tex], let's compare the slopes of these two lines.
1. Identify the slope:
- For the line [tex]\( y = m x - 4 \)[/tex], the slope is [tex]\( m \)[/tex].
- For the line [tex]\( y = x - 4 \)[/tex], the slope is [tex]\( 1 \)[/tex].
2. Set up the comparison:
- We need to find out when the slope [tex]\( m \)[/tex] is less than the slope [tex]\( 1 \)[/tex] of the line [tex]\( y = x - 4 \)[/tex].
3. Formulate the condition:
- The inequality that represents our condition is [tex]\( m < 1 \)[/tex].
4. Evaluate the options:
- [tex]\( m = -1 \)[/tex]: This means [tex]\( m \)[/tex] is definitely less than 1.
- [tex]\( m = 1 \)[/tex]: This means [tex]\( m \)[/tex] is equal to 1, not less than 1.
- [tex]\( m < 1 \)[/tex]: This directly matches our condition.
- [tex]\( m > 1 \)[/tex]: This means [tex]\( m \)[/tex] is greater than 1, which contradicts our condition.
Therefore, the correct statement about [tex]\( m \)[/tex] is:
[tex]\[ m < 1 \][/tex]
Thus, the choice that corresponds to this condition is:
[tex]\[ \boxed{3} \][/tex]
