Video: Graphs of Linear Inequalities

Which of the following figures is the correct graph of 𝑦 ≥ 𝑥? [A] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E.

02:07

Video Transcript

Which of the following figures is the correct graph of 𝑦 is greater than or equal to 𝑥 or 𝑦 is more than or equal to 𝑥?

The first thing to notice in this question is that all five of the graphs have the line 𝑦 equals 𝑥 drawn. Therefore, we need to focus on the inequality sign. 𝑦 is greater than or equal to 𝑥.

Anytime we wish to draw an inequality on a coordinate axis, we need to shade the correct region. This means we can immediately eliminate graph B as there is no shading involved. It is just the line 𝑦 equals 𝑥.

If our inequality sign is greater than or equal to, i.e., 𝑦 is greater than or equal to 𝑥 or 𝑦 is greater than 𝑥, we shade above the line. This is because any ordered pairs or coordinates above the line 𝑦 equals 𝑥 will have a 𝑦-coordinate greater than the 𝑥-coordinate.

In a similar way, had the equation been 𝑦 is less than or equal to 𝑥 or 𝑦 is less than 𝑥, we would shade below the line because the 𝑦-coordinates are less than the 𝑥-coordinates anywhere below the line 𝑦 equals 𝑥. This means that we can eliminate graph D and graph E.

Our final decision is whether the inequality 𝑦 is greater than or equal to 𝑥 is shown by graph A or graph C. Well, graph A actually shows 𝑦 is greater than 𝑥 because we have a dotted line, whereas graph C shows the correct equation 𝑦 is greater than or equal to 𝑥 because we have a continuous or bold line. Therefore, by eliminating all the other possibilities, we can see that the correct figure or graph of the inequality 𝑦 is greater than or equal to 𝑥 is graph C.

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