Question

Which of the following ordered pairs are part of the solution set for the linear inequality y≥−3x+4 ?(1 point)


A. (3,0)
B. (2,-2)
C. (0,2)
D. (4,-1)
E. (0,3)

Answer 1

To determine which of the ordered pairs are part of the solution set for the linear inequality \( y \geq -3x + 4 \), we can substitute the \( x \) and \( y \) values from the ordered pairs into the inequality and check if the inequality holds true.

1. **For \( (3, 0) \)**:
\[
0 \geq -3(3) + 4 \implies 0 \geq -9 + 4 \implies 0 \geq -5 \quad \text{(True)}
\]

2. **For \( (2, -2) \)**:
\[
-2 \geq -3(2) + 4 \implies -2 \geq -6 + 4 \implies -2 \geq -2 \quad \text{(True)}
\]

3. **For \( (0, 2) \)**:
\[
2 \geq -3(0) + 4 \implies 2 \geq 0 + 4 \implies 2 \geq 4 \quad \text{(False)}
\]

4. **For \( (4, -1) \)**:
\[
-1 \geq -3(4) + 4 \implies -1 \geq -12 + 4 \implies -1 \geq -8 \quad \text{(True)}
\]

5. **For \( (0, 3) \)**:
\[
3 \geq -3(0) + 4 \implies 3 \geq 0 + 4 \implies 3 \geq 4 \quad \text{(False)}
\]

Thus, the pairs that satisfy the inequality \( y \geq -3x + 4 \) are:

- A. \( (3, 0) \)
- B. \( (2, -2) \)
- D. \( (4, -1) \)

**Correct ordered pairs: A, B, D.**