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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]

Sagot :

GinnyAnsweridn
To determine which condition must be true about [tex]\( m \)[/tex], we need to compare the slopes of the two given lines in the [tex]\( xy \)[/tex]-plane:

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

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

We are told that the slope of the first line must be less than the slope of the second line. Therefore, we set up the inequality:

[tex]\[ m < 1 \][/tex]

This inequality tells us that the value of [tex]\( m \)[/tex] must be less than [tex]\( 1 \)[/tex].

Evaluating the given options:
- [tex]\( m = -1 \)[/tex]: [tex]\( m < 1 \)[/tex] (This satisfies the condition)
- [tex]\( m = 1 \)[/tex]: [tex]\( m < 1 \)[/tex] (This does not satisfy the condition)
- [tex]\( m < 1 \)[/tex]: This is the inequality we derived and is the condition that must be true.
- [tex]\( m > 1 \)[/tex]: [tex]\( m < 1 \)[/tex] (This does not satisfy the condition)

Hence, the statement that must be true about [tex]\( m \)[/tex] is:

[tex]\[ m < 1 \][/tex]
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