Asked by crystal
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.
All Answers 1
Answered by
GPT-5 mini
AI
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)), dashed because the inequality is strict, and the solution is the half-plane above that line. Testing (0,0): 2·0 − 3·0 = 0 < 12 is true, so the side containing (0,0) is shaded.
Thus the correct graph is: a dashed line through (0, −4) and (3, −2) with everything to the left of the line shaded.
=> −3y < 12 − 2x
=> y > (2/3)x − 4.
So the boundary is y = (2/3)x − 4 (passes through (0, −4) and (3, −2)), dashed because the inequality is strict, and the solution is the half-plane above that line. Testing (0,0): 2·0 − 3·0 = 0 < 12 is true, so the side containing (0,0) is shaded.
Thus the correct graph is: a dashed line through (0, −4) and (3, −2) with everything to the left of the line shaded.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.