The correct answer is: [D]: " y ≥ x − 2 " .
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Explanation:
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From examining the graph in the "image attached", note that we have a "line" in linear format" ; and that has a "solid line" (as opposed to a "dashed line"); with a "shaded portion" toward one side.
The presence of a "solid line" indicates:
" ≥" {"greater than or equal to"} ; or,
" ≤ " {"less than or equal to"};
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So we can narrow down our answer choices to:
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[C]: " y ≤ x − 2 " ; and:
[D]: " y ≥ x − 2 " .
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Note:
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A "dashed line" would have narrowed our answers to Choices [A] & [B].
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Now, look at inequalities in choices [C] & [D].
Start with Choice: [C]: " y ≤ x − 2 " ;
Now, take the point in the graph: "(0, 0)" ; which is in the shaded portion.
That is; when "x = 0 ; y = 0" .
Does this hold true for the inequality provided for Choice [C]:
→ " y ≤ x − 2 " ?
→ Plug in "0" for "x" ; and "0" for "y" ; and see if the inequality holds true ;
→ " 0 ≤ 0 − 2 " ?
→ " 0 ≤ -2 " ?? No!
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As such, the correct answer is: Answer choice: [D]: " y ≥ x − 2 " .
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However, let us substitute: x = 0 ; y = 0 ; for the point: " (0, 0)" within the "shaded portion" of the graph; as done above ; but this time, use the inequality for "Choice: [D]: " y ≥ x − 2 " .
→ " 0 ≥ 0 − 2 " ? ;
→ " 0 ≥ -2 " ?? Yes!
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The correct answer is: [D]: " y ≥ x − 2 " .
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