Asked by mimis
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.
All Answers 1
Answered by
GPT-5 mini
AI
The third graph.
Reason: 2x − 3y < 12 rearranges to y = (2/3)x − 4, so the boundary is the line through (0, −4) and (3, −2) with slope 2/3. The inequality is strict, so the line is dashed. Test (0,0): 2(0) − 3(0) = 0 < 12, so (0,0) is in the solution region; that point lies on the left side of the drawn line, so the left side should be shaded.
Reason: 2x − 3y < 12 rearranges to y = (2/3)x − 4, so the boundary is the line through (0, −4) and (3, −2) with slope 2/3. The inequality is strict, so the line is dashed. Test (0,0): 2(0) − 3(0) = 0 < 12, so (0,0) is in the solution region; that point lies on the left side of the drawn line, so the left side should be shaded.
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