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Solve the following problem and select your answer from the choices given.

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 solve this problem, let's start by understanding the slopes of the given lines.

1. Identify the slope of the line [tex]\( y = mx - 4 \)[/tex]:
- A line in the form [tex]\( y = mx + b \)[/tex] has a slope [tex]\( m \)[/tex].
- Thus, the slope of the line [tex]\( y = mx - 4 \)[/tex] is [tex]\( m \)[/tex].

2. Identify the slope of the line [tex]\( y = x - 4 \)[/tex]:
- Again, a line in the form [tex]\( y = mx + b \)[/tex] has a slope [tex]\( m \)[/tex].
- Here, [tex]\( y = x - 4 \)[/tex] can be written as [tex]\( y = 1 \cdot x - 4 \)[/tex].
- Therefore, the slope of this line is [tex]\( 1 \)[/tex].

3. Compare the slopes of the two lines:
- We need to determine the condition under which the slope of the line [tex]\( y = mx - 4 \)[/tex] is less than the slope of the line [tex]\( y = x - 4 \)[/tex].
- Mathematically, this is: [tex]\( m < 1 \)[/tex].

Thus, the correct answer is:

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

So, the condition that must be true about [tex]\( m \)[/tex] is [tex]\( m < 1 \)[/tex]. The corresponding choice is:

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