sweetnessnbab
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Which point is a solution to [tex]$y \leq 3x - 4$[/tex]?

A. [tex]$(0, 4)$[/tex]
B. [tex]$(3, 1)$[/tex]
C. [tex]$(-2, 0)$[/tex]
D. [tex]$(0, 0)$[/tex]

Sagot :

GinnyAnswer
To determine which point \( (x, y) \) satisfies the inequality \( y \leq 3x - 4 \), we need to check each of the given points one by one.

1. Point A: \( (0,4) \)
- Substitute \( x = 0 \) and \( y = 4 \) into the inequality:
[tex]\[ y \leq 3x - 4 \][/tex]
[tex]\[ 4 \leq 3(0) - 4 \][/tex]
[tex]\[ 4 \leq -4 \][/tex]
- This inequality is false.

2. Point B: \( (3,1) \)
- Substitute \( x = 3 \) and \( y = 1 \) into the inequality:
[tex]\[ y \leq 3x - 4 \][/tex]
[tex]\[ 1 \leq 3(3) - 4 \][/tex]
[tex]\[ 1 \leq 9 - 4 \][/tex]
[tex]\[ 1 \leq 5 \][/tex]
- This inequality is true.

3. Point C: \( (-2,0) \)
- Substitute \( x = -2 \) and \( y = 0 \) into the inequality:
[tex]\[ y \leq 3x - 4 \][/tex]
[tex]\[ 0 \leq 3(-2) - 4 \][/tex]
[tex]\[ 0 \leq -6 - 4 \][/tex]
[tex]\[ 0 \leq -10 \][/tex]
- This inequality is false.

4. Point D: \( (0,0) \)
- Substitute \( x = 0 \) and \( y = 0 \) into the inequality:
[tex]\[ y \leq 3x - 4 \][/tex]
[tex]\[ 0 \leq 3(0) - 4 \][/tex]
[tex]\[ 0 \leq -4 \][/tex]
- This inequality is false.

Among the given points, only Point B: \( (3,1) \) satisfies the inequality \( y \leq 3x - 4 \).

Therefore, the answer is:
B. [tex]\( (3,1) \)[/tex]
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