Question

In which quadrants do solutions for the inequality y≤x-4 exist?

OI, III, and IV
OI, II, and III
OI and IV
All four quadrants

Answer 1

(a) I, III, and IV

Explanation:

We want to identify areas on a graph where the solutions to an inequality might be found.

Boundary line

The boundary line for the inequality y ≤ 2/3x -4 has a positive slope and a negative y-intercept. That means it must pass through quadrants I, III, and IV.

Solution set

Quadrant II is above the line, but the y ≤ () inequality tells you the shading is below the line, where y-values are less than those on the line. There can be no solutions in quadrant II.

Solutions are found in quadrants I, III, and IV.

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For reference, the second attachments shows the quadrant numbering.