Answered

In the [tex]$xy$[/tex]-plane, the slope of the line [tex]$y=mx-4$[/tex] is less than the slope of the line [tex]$y=x-4$[/tex]. Which of the following must be true about [tex]$m$[/tex]?

A. [tex]$m = -1$[/tex]
B. [tex]$m = 1$[/tex]
C. [tex]$m \ \textless \ 1$[/tex]
D. [tex]$m \ \textgreater \ 1$[/tex]



Answer :

GinnyAnswer
To solve the problem, let's carefully compare the slopes of the given lines:

1. We have two lines:
- The first line is [tex]\( y = mx - 4 \)[/tex].
- The second line is [tex]\( y = x - 4 \)[/tex].

2. The general form of a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

3. For the first line [tex]\( y = mx - 4 \)[/tex]:
- The slope is [tex]\( m \)[/tex].

4. For the second line [tex]\( y = x - 4 \)[/tex]:
- The slope is [tex]\( 1 \)[/tex] because [tex]\( y = x - 4 \)[/tex] can be rewritten as [tex]\( y = 1x - 4 \)[/tex].

5. 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].
- This means [tex]\( m \)[/tex] is less than [tex]\( 1 \)[/tex].

6. Therefore, the condition that must be true is:
[tex]\[ m < 1 \][/tex]

So out of the given options, [tex]\( m < 1 \)[/tex] is the correct answer.