kahowton
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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 this question, let's compare the slopes of the two given lines.

1. The equation of the first line is [tex]\(y = mx -4\)[/tex].
- The slope of this line is [tex]\(m\)[/tex].

2. The equation of the second line is [tex]\( y = x - 4\)[/tex].
- The slope of this line is [tex]\(1\)[/tex].

The problem states that 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 have the inequality:
[tex]\[ m < 1 \][/tex]

Thus, the correct condition is that [tex]\( m \)[/tex] must be less than [tex]\( 1 \)[/tex].

So, the answer is:
[tex]\[ m < 1 \][/tex]

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