N/A — Exam

Question 17 • Mathematics I

Which is the graph of the linear inequality 6 x plus 2 y is greater than negative 10 ?

Answer

Image with description On a coordinate plane, a dashed straight line with negative slope goes through (negative 2 comma 1) and (0 comma negative 5). Everything to the right of the line is shaded.

Image with description On a coordinate plane, a dashed straight line with positive slope goes through (0 comma negative 5) and (2 comma 1). Everything to the right of the line is shaded.

Image with description On a coordinate plane, a dashed straight line with negative slope goes through (0 comma 5) and (2 comma negative 1). Everything to the right of the line is shaded.

Image with description On a coordinate plane, a dashed straight line with negative slope goes through (0 comma 5) and (negative 2 comma negative 1). Everything to the right of the line is shaded.

Explanation

Rearrange the inequality: 6x + 2y > −10 becomes y > −3x − 5. The boundary is a dashed line because the inequality is strict; it has slope −3 and passes through (0, −5) and (−2, 1). This matches choice A, whose shading includes (0, 0), a point that satisfies the inequality.

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