Which is the graph of the linear inequality 1 half x minus 2 y is greater than negative 6 ?

Answer

A

Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A solid straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything above the line is shaded.

B

Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A solid straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything above the line is shaded.

C

Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A dashed straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything below the line is shaded.

D

Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A solid straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything above the line is shaded.

Explanation

Rearrange the inequality: ½x − 2y > −6 gives −2y > −6 − ½x. Dividing by −2 reverses the inequality, so y < 3 + ¼x. The boundary line has slope ¼ and passes through (−4, 2) and (4, 4); because the inequality is strict, the line is dashed, and because y is less than the line, the region below it is shaded. This matches choice C.

AI-written and checked against the verified answer.

Pretest

Which is the graph of the linear inequality 1 half x minus 2 y is greater than negative 6 ?

Explanation

More from this Course