Graphing Two-Variable Linear Inequalities — Quiz

Question 7 • Mathematics I

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

Answer

Image with description On a coordinate plane, a dashed straight line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the right of the line is shaded.

Image with description On a coordinate plane, a dashed straight line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the left of the line is shaded.

Image with description On a coordinate plane, a solid straight line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything 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 (0 comma negative 4) and (3 comma negative 2). Everything to the left of the line is shaded.

Explanation

Rewrite the inequality by solving for y: 2x − 3y < 12 gives y > (2/3)x − 4, since dividing by −3 reverses the inequality. The boundary is the dashed line through (0, −4) and (3, −2), and the solution is the region above the line, which is shown to its left. Therefore, the correct choice is the dashed line shaded to the left.

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