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On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
Which point is a solution to the linear inequality y < Negative one-halfx + 2?

(2, 3)
(2, 1)
(3, –2)
(–1, 3)



Answer :

mhanifa

The point (3, -2)

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Insert each point into the inequality and see if it makes the inequality true.

For point (2, 3), if we plug it into the inequality:

  • 3 < (-1/2)*2 + 2 ⇒ 3 < 1, which is false

For point (2, 1), if we plug it in:

  • 1 < (-1/2)*2 + 2 ⇒ 1 < 1, which is false

For point (3, -2), if we plug it in:

  • -2 < (-1/2)*3 + 2 ⇒ -2 < 0.5, which is true

For point (-1, 3), if we plug it in:

  • 3 < (-1/2)*(-1)+ 2 ⇒ 3 < 2.5, which is false.

Thus, the point that satisfies the inequality is (3, -2).