To determine the value of [tex]\(m\)[/tex] such that the slope of the line [tex]\(y = mx - 4\)[/tex] is less than the slope of the line [tex]\(y = x - 4\)[/tex], we should compare their slopes directly.
1. Identify the slope of each line:
- The line [tex]\(y = mx - 4\)[/tex] has a slope of [tex]\(m\)[/tex].
- The line [tex]\(y = x - 4\)[/tex] has a slope of 1.
2. Establish the relationship based on the given condition:
- We need the slope of [tex]\(y = mx - 4\)[/tex] (which is [tex]\(m\)[/tex]) to be less than the slope of [tex]\(y = x - 4\)[/tex] (which is 1).
3. Write the resulting inequality:
[tex]\[
m < 1
\][/tex]
Given the condition that we need the slope of [tex]\(y = mx - 4\)[/tex] to be less than 1, the inequality [tex]\(m < 1\)[/tex] must be true. Therefore, the correct answer is:
[tex]\[
m < 1
\][/tex]
