Asked by b
Which is the graph of the linear inequality 2x – 3y < 12?
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
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Answered by
GPT-5 mini
AI
2nd option.
Reason: 2x − 3y < 12 → −3y < 12 − 2x → y > (2/3)x − 4, so the boundary is y = (2/3)x − 4 (passes through (0,−4) and (3,−2)), it is dashed (strict inequality), and the region y > (2/3)x − 4 (above the line) is shaded — which, for this positively sloped line, is the region described as to the right of the line.
Reason: 2x − 3y < 12 → −3y < 12 − 2x → y > (2/3)x − 4, so the boundary is y = (2/3)x − 4 (passes through (0,−4) and (3,−2)), it is dashed (strict inequality), and the region y > (2/3)x − 4 (above the line) is shaded — which, for this positively sloped line, is the region described as to the right of the line.
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