Graphing Two-Variable Linear Inequalities — Quiz

Question 5 • Mathematics I

Which is the graph of the linear inequality y is greater than or equal to negative x minus 3 ?

Answer

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

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

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

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

Explanation

Because the inequality includes “greater than or equal to,” the boundary line is solid. The line y = −x − 3 passes through (−3, 0) and (0, −3). Test the point (0, 0): it satisfies 0 ≥ −3, so the shaded region must include the origin. That is the region to the right of the line, shown in choice D.

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