To determine which point is a solution to the inequality [tex]\( y \leq 3x - 4 \)[/tex], we need to check each point individually by substituting the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values into the inequality.
Let's examine each point:
### Point A: [tex]\((0, 4)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 4 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 4 \leq 3(0) - 4 \][/tex]
[tex]\[ 4 \leq -4 \][/tex]
This is not true. Therefore, [tex]\((0, 4)\)[/tex] is not a solution.
### Point B: [tex]\((3, 1)\)[/tex]
Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 1 \)[/tex] 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 is true. Therefore, [tex]\((3, 1)\)[/tex] is a solution.
### Point C: [tex]\((0, 0)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 0 \leq 3(0) - 4 \][/tex]
[tex]\[ 0 \leq -4 \][/tex]
This is not true. Therefore, [tex]\((0, 0)\)[/tex] is not a solution.
### Point D: [tex]\((-2, 0)\)[/tex]
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 0 \)[/tex] 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 is not true. Therefore, [tex]\((-2, 0)\)[/tex] is not a solution.
Based on the above calculations, the point that satisfies the inequality [tex]\( y \leq 3x - 4 \)[/tex] is:
[tex]\[ \boxed{(3, 1)} \][/tex]
