Which is the graph of the linear inequality 2 x minus 3 y is less than 12 ?

Answer

A

Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A dashed line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the right of the line is shaded.

B

Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A solid line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the right of the line is shaded.

C

Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A dashed line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the left of the line is shaded.

D

Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A solid line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the left of the line is shaded.

Explanation

Rearrange 2x − 3y < 12 to get y > (2/3)x − 4; dividing by −3 reverses the inequality sign. The boundary is therefore a dashed line with y-intercept −4 and slope 2/3, passing through (0, −4) and (3, −2). The solution region is above the line, which is the region to its left, so choice C is correct.

AI-written and checked against the verified answer.

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Which is the graph of the linear inequality 2 x minus 3 y is less than 12 ?

Explanation

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