To determine which values of [tex]\( m \)[/tex] satisfy the condition that the slope of the line [tex]\( y = mx - 4 \)[/tex] is less than the slope of the line [tex]\( y = x - 4 \)[/tex], follow these steps:
1. Identify the slopes of the given lines:
- The line [tex]\( y = mx - 4 \)[/tex] has a slope [tex]\( m \)[/tex].
- The line [tex]\( y = x - 4 \)[/tex] has a slope of [tex]\( 1 \)[/tex] because it is in the standard linear form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope.
2. Set up the inequality:
- We are given that the slope of [tex]\( y = mx - 4 \)[/tex] is less than the slope of [tex]\( y = x - 4 \)[/tex].
- This translates to [tex]\( m < 1 \)[/tex].
3. Evaluate the given options to see which satisfy [tex]\( m < 1 \)[/tex]:
- [tex]\( m = -1 \)[/tex]: This fits the condition because [tex]\(-1 < 1\)[/tex].
- [tex]\( m = 1 \)[/tex]: This does not fit the condition because [tex]\( 1 \)[/tex] is not less than [tex]\( 1 \)[/tex].
- [tex]\( m < 1 \)[/tex]: This directly states the condition we derived.
- [tex]\( m > 1 \)[/tex]: This does not fit the condition because values greater than [tex]\( 1 \)[/tex] do not satisfy [tex]\( m < 1 \)[/tex].
Therefore, the statements that must be true about [tex]\( m \)[/tex] are [tex]\( m = -1 \)[/tex] and [tex]\( m < 1 \)[/tex].
