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

Question

?(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).