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

Question

Responses

(3,0)
(3,0)

(2,-2)
(2,-2)

(0,2)
(0,2)

(0,3)
(0,3)

(4,-1)

Answer 1

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

1. For (3, 0):

   • Substitute: \( 0 \geq -3(3) + 4 \)
   • Simplifying: \( 0 \geq -9 + 4 \)
   • \( 0 \geq -5 \) (true)

2. For (2, -2):

   • Substitute: \( -2 \geq -3(2) + 4 \)
   • Simplifying: \( -2 \geq -6 + 4 \)
   • \( -2 \geq -2 \) (true)

3. For (0, 2):

   • Substitute: \( 2 \geq -3(0) + 4 \)
   • Simplifying: \( 2 \geq 0 + 4 \)
   • \( 2 \geq 4 \) (false)

4. For (0, 3):

   • Substitute: \( 3 \geq -3(0) + 4 \)
   • Simplifying: \( 3 \geq 0 + 4 \)
   • \( 3 \geq 4 \) (false)

5. For (4, -1):

   • Substitute: \( -1 \geq -3(4) + 4 \)
   • Simplifying: \( -1 \geq -12 + 4 \)
   • \( -1 \geq -8 \) (true)

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

• (3, 0)
• (2, -2)
• (4, -1)