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]
