Question

Which is the graph of linear inequality 6x + 2y > –10?

On a coordinate plane, a dashed straight line with negative slope goes through (negative 2, 0) and (0, negative 6). Everything to the right of the line is shaded.

On a coordinate plane, a dashed straight line with negative slope goes through (0, 6) and (2, 0). Everything to the right of the line is shaded.

On a coordinate plane, a dashed straight line with positive slope goes through (0, negative 6) and (2, 0). Everything to the right of the line is shaded.

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

Answer 1

Solve for y: 6x + 2y > −10 ⇒ 2y > −6x −10 ⇒ y > −3x −5.

So the boundary is the line y = −3x −5 (slope −3), and it is dashed because the inequality is strict (>). The shaded side is the half-plane above/to the right of that line (e.g. (0,0) satisfies 0 > −5, so the origin must be shaded).

The choice that matches a dashed line with negative slope and shading that includes the origin is the first option (the dashed line with negative slope through (−2,0) and (0,−6), shading to the right).