Graphing Two-Variable Linear Inequalities — Quiz

Question 6 • Mathematics I

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

Answer

Image with description On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4 comma 2) and (4 comma 4). Everything above and to the left of the line is shaded.

Image with description On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4 comma 2) and (4 comma 4). Everything below and to the right of the line is shaded.

Image with description On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4 comma 2) and (4 comma 4). Everything above and to the left of the line is shaded.

Explanation

Rearrange ½x − 2y > −6 to isolate y: dividing by −2 reverses the inequality, giving y < ¼x + 3. The boundary is therefore dashed, and the solution region is below the line. The line passes through (−4, 2) and (4, 4), so choice C matches.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz