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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything below the line is shaded.
Which points are solutions to the linear inequality y < 0.5x + 2? Select three options.


(–3, –2)
(–2, 1)
(–1, –2)
(–1, 2)
(1, –2)

Sagot :

semsee45

Answer:

(-3, -2)

(-1, -2)

(1, -2)

Step-by-step explanation:

To determine which points are solutions to the linear inequality y < 0.5x + 2, we need to check each point by substituting the x and y coordinates into the inequality.

Given points:

  • (-3, -2)
  • (-2, 1)
  • (-1, -2)
  • (-1, 2)
  • (1, -2)

Let's test each point:

For point (-3, -2):

[tex]y < 0.5x + 2 \\\\-2 < 0.5(-3) + 2 \\\\-2 < -1.5 + 2 \\\\-2 < 0.5 \quad \text{(True)}[/tex]

For point (-2, 1):

[tex]y < 0.5x + 2 \\\\1 < 0.5(-2) + 2 \\\\1 < -1 + 2 \\\\1 < 1 \quad \text{(False)}[/tex]

For point (-1, -2):

[tex]y < 0.5x + 2 \\\\-2 < 0.5(-1) + 2 \\\\-2 < -0.5 + 2 \\\\-2 < 1.5 \quad \text{(True)}[/tex]

For point (-1, 2):

[tex]y < 0.5x + 2 \\\\2 < 0.5(-1) + 2 \\\\2 < -0.5 + 2 \\\\2 < 1.5 \quad \text{(False)}[/tex]

For point (1, -2):

[tex]y < 0.5x + 2 \\\\-2 < 0.5(1) + 2 \\\\-2 < 0.5 + 2 \\\\-2 < 2.5 \quad \text{(True)}[/tex]

Therefore, the points that are solutions to the inequality y < 0.5x + 2 are:

  • (-3, -2)
  • (-1, -2)
  • (1, -2)

When determining solutions using the graph of the given inequality:

  • Points inside the shaded region satisfy the inequality and are solutions.
  • Points on the boundary line do not satisfy the inequality and are not solutions because the inequality is strict (< or >).
  • Points outside the shaded region do not satisfy the inequality and are not solutions.
View image semsee45
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