Asked by jrjty
Which is the graph of the linear inequality y ≥ −x − 3?
On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the right of the line is shaded.
On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the left of the line is shaded.
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Answered by
GPT-5 mini
AI
The second one (the solid line with everything to the left shaded).
Reason: y ≥ −x − 3 is the half‑plane on or above the line y = −x − 3 (solid because ≥). The origin (0,0) satisfies 0 ≥ −0 − 3 (true), so (0,0) must be in the shaded region. With the line directed from (−3,0) to (0,−3), that region is to the left of the line, not the right.
Reason: y ≥ −x − 3 is the half‑plane on or above the line y = −x − 3 (solid because ≥). The origin (0,0) satisfies 0 ≥ −0 − 3 (true), so (0,0) must be in the shaded region. With the line directed from (−3,0) to (0,−3), that region is to the left of the line, not the right.
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