Let's analyze the given problem by breaking it down step by step:
1. Identify the slope of each line:
- The general equation of a line in slope-intercept form is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope.
- For the first given line [tex]\( y = mx - 4 \)[/tex]:
- The slope is [tex]\( m \)[/tex].
- For the second given line [tex]\( y = x - 4 \)[/tex]:
- The slope is the coefficient of [tex]\( x \)[/tex], which is 1.
2. Compare the slopes:
- We are given that the slope of the first line ([tex]\( m \)[/tex]) is less than the slope of the second line (1).
- Mathematically, this can be written as:
[tex]\[
m < 1
\][/tex]
3. Determine the correct condition for [tex]\( m \)[/tex]:
- From the inequality [tex]\( m < 1 \)[/tex], we need to identify which given option matches this condition. Let's assess each provided option:
[tex]\[
m = -1 \quad \text{(This value satisfies} \ m < 1 \text{)}
\][/tex]
[tex]\[
m = 1 \quad \text{(This value does not satisfy} \ m < 1 \text{)}
\][/tex]
[tex]\[
m < 1 \quad \text{(This statement itself is exactly the condition we derived)}
\][/tex]
[tex]\[
m > 1 \quad \text{(This value does not satisfy} \ m < 1 \text{)}
\][/tex]
4. Conclusion:
- The correct condition that matches our derived inequality [tex]\( m < 1 \)[/tex] is clearly stated in the option [tex]\( m < 1 \)[/tex].
Therefore, the answer is:
[tex]\[ \boxed{m < 1} \][/tex]
