Question 15

−x≤y≤3x

The inequality represented in the graph is −x≤y≤3x, which shows that y is bounded between the lines y = -x and y = 3x.

A) x≤y≤3x

This option suggests that y is at least as large as x and at most 3 times x. However, the graph does not represent this range, as the lower boundary is not at y = x but rather at y = -x.

B) x≥y≥3x

This choice indicates that y is less than or equal to x and also less than or equal to 3x. The graph does not reflect this situation, as it visually represents a different range for y that includes values greater than x.

C) −x≤y≤3x

This is the correct option as it accurately describes the region shaded in the graph. The area between the lines y = -x and y = 3x demonstrates that y lies within these bounds.

D) −x≥y≥3x

This option implies that y is simultaneously greater than or equal to -x and less than or equal to 3x. This is incorrect as the graph does not show y being greater than -x, rather it is bounded below by -x.

Conclusion

The correct answer, −x≤y≤3x, is definitively right as it aligns perfectly with the graphical representation of the shaded region. All other options fail to capture the correct relationships and boundaries depicted in the graph, illustrating that y falls between the two specified lines.