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

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Video Transcript

Which of the following figures is the correct graph of 𝑦 equals 𝑥? Is it graph A, graph B, graph C, graph D, or graph E?

All five graphs show the equation 𝑦 equals 𝑥, as they have an intercept of zero and a gradient of one. However, as graphs A, B, C, and E have a shaded region, they all contain an inequality and not an equality.

This means that the figure that shows the graph of 𝑦 equals 𝑥 is figure D. As figures A and B have an area shaded above the line 𝑦 equals 𝑥, the 𝑦 must be greater than 𝑥.

In figure A, there is a bold line this means the inequality that is shown in figure A is 𝑦 is greater than or equal to 𝑥.

In figure B, as we have a dotted line, we can say that 𝑦 is greater than 𝑥. In the same way, figure C shows that 𝑦 is less than 𝑥 as we have shaded below the line and we have a dotted line.

Figure E shows that 𝑦 is less than or equal to 𝑥 as we have a bold line and, once again, have shaded below the line 𝑦 equals 𝑥. This means that figures A, B, C, and E show inequalities whereas figure D shows the equation 𝑦 equals 𝑥.

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