To solve this problem, we need to analyze the slopes of the given lines in the [tex]\(xy\)[/tex]-plane and compare them. We are given two lines:
1. [tex]\( y = mx - 4 \)[/tex]
2. [tex]\( y = x - 4 \)[/tex]
### Step-by-Step Solution:
1. Identify the slopes:
- The slope of a line in the form [tex]\( y = mx + b \)[/tex] is given by the coefficient of [tex]\( x \)[/tex], which is [tex]\( m \)[/tex].
- The slope of the line [tex]\( y = mx - 4 \)[/tex] is [tex]\( m \)[/tex].
- The slope of the line [tex]\( y = x - 4 \)[/tex] is [tex]\( 1 \)[/tex] since it can be written as [tex]\( y = 1x - 4 \)[/tex].
2. Compare the slopes:
- According to the problem, the slope of the line [tex]\( y = mx - 4 \)[/tex] is less than the slope of the line [tex]\( y = x - 4 \)[/tex].
Therefore, we can write the inequality:
[tex]\[
m < 1
\][/tex]
3. Interpret the inequality:
- This inequality [tex]\( m < 1 \)[/tex] means that the value of [tex]\( m \)[/tex] must be less than [tex]\( 1 \)[/tex].
### Conclusion:
The correct interpretation of the question is that for the slope of the line [tex]\( y = mx - 4 \)[/tex] to be less than the slope of the line [tex]\( y = x - 4 \)[/tex], the value of [tex]\( m \)[/tex] must be less than [tex]\( 1 \)[/tex].
Thus, the answer is:
[tex]\[
m < 1
\][/tex]
