Video Transcript
Consider the inequalities shown in Figure 1 and Figure 2. Which of the following is correct? Is it option (A) Figure 1 shows 𝑦 is greater than or equal to 𝑥 and Figure 2 shows 𝑦 is greater than 𝑥 or option (B) Figure 1 shows 𝑦 is greater than 𝑥 and Figure 2 shows 𝑦 is greater than or equal to 𝑥?
We know that an inequality can be represented graphically as a region on one side of a line. In both figures in this question, the line drawn corresponds to the equation 𝑦 is equal to 𝑥. The lines pass through the origin zero, zero and have a gradient or slope equal to one. Inequalities that use the less than or greater than symbol are plotted with a dashed line to show that the line is not included in the region. A bold line, on the other hand, represents the inequality signs greater than or equal to or less than or equal to. This indicates that the line is included in the region.
Figure 1 therefore represents the inequality 𝑦 is strictly greater than 𝑥, whereas Figure 2 represents the inequality 𝑦 is greater than or equal to 𝑥. This means that the correct answer is option (B) Figure 1 shows 𝑦 is greater than 𝑥 and Figure 2 shows 𝑦 is greater than or equal to 𝑥.
Note that these inequalities are greater than and greater than or equal to as opposed to less than and less than or equal to as the region shaded is above the line. The 𝑦-values in the shaded region will be greater than or greater than or equal to the 𝑥-values.
