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
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
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.