(3, -2) and (2, 1) are solutions to the inequality y <= 3/2x - 1
How to determine the inequality?
The complete question is added as an attachment
The points are given as:
(3, -2) and (2, 1)
Next, we test the points on each inequality in the list of options.
So, we have:
Option 1
y > 1/2x + 2
Substitute (3, -2) and (2, 1) for x and y
-2 > 1/2 * 3 + 2 ⇒ -2 > 3.5 -- false
2 > 1/2 * 1 + 2 ⇒ 2 > 2.5 -- false
Hence, (3, -2) and (2, 1) are not solutions to the inequality y > 1/2x + 2
Option 2
y <= 3/2x - 1
Substitute (3, -2) and (2, 1) for x and y
-2 <= 3/2 * 3 - 1 ⇒ -2 <= 3.5 -- true
1 <= 3/2 * 2 - 1 ⇒ 1 < 2 -- true
Hence, (3, -2) and (2, 1) are solutions to the inequality y <= 3/2x - 1
Option 3
y >= 4x - 2
Substitute (3, -2) and (2, 1) for x and y
-2 >= 4 * 3 - 2 ⇒ -2 >= 10 -- false
2 <= 4 * 2 - 2 ⇒ 2 <= 6 -- false
Hence, (3, -2) and (2, 1) are not solutions to the inequality y >= 4x - 2
Option 4
y < -2x + 1
Substitute (3, -2) and (2, 1) for x and y
-2 < -2 * 3 + 1 ⇒ -2 < -5 -- false
2 < -2 * 2 + 1 ⇒ 2 < -3 -- false
Hence, (3, -2) and (2, 1) are not solutions to the inequality y < -2x + 1
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