Question

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

(4,-1)
(4,-1)
(2,-2)
(2,-2)
(0,2)
(0,2)
(3,0)
(3,0)
(0,3)

Answer 1

To determine which ordered pairs satisfy the inequality \( y \geq -3x + 4 \), we can substitute the \( x \) and \( y \) values from each ordered pair into the inequality and check if the inequality holds true.

1. **(4, -1)**:
Check: \(-1 \geq -3(4) + 4\)
\(-1 \geq -12 + 4\)
\(-1 \geq -8\) (True)

2. **(2, -2)**:
Check: \(-2 \geq -3(2) + 4\)
\(-2 \geq -6 + 4\)
\(-2 \geq -2\) (True)

3. **(0, 2)**:
Check: \(2 \geq -3(0) + 4\)
\(2 \geq 0 + 4\)
\(2 \geq 4\) (False)

4. **(3, 0)**:
Check: \(0 \geq -3(3) + 4\)
\(0 \geq -9 + 4\)
\(0 \geq -5\) (True)

5. **(0, 3)**:
Check: \(3 \geq -3(0) + 4\)
\(3 \geq 0 + 4\)
\(3 \geq 4\) (False)

**Conclusion**: The ordered pairs that are part of the solution set for the inequality \( y \geq -3x + 4 \) are:

- (4, -1)
- (2, -2)
- (3, 0)

So, the pairs that satisfy the inequality are (4, -1), (2, -2), and (3, 0).