Two-Variable Linear Inequalities — Quiz

Question 4 • Algebra: Concepts and Connections

Which graph represents y is less than or equal to negative 3 x ?

Answer

Image with description On a coordinate plane, the x-axis labeled "x" ranges from negative 5 to 5 in increments of 1, and the y-axis labeled "y" ranges from negative 5 to 5 in increments of 1.The line passes through the quadrants 1, and 3, passing through the points "negative 1 comma negative 3","0 comma 0" and "1 comma 3". Both ends of the line terminate with arrowheads at "negative 1 point 5 comma 5" and "1 point 5 comma negative 5". The entire region to the right of the line is shaded in a light tan color, representing a half-plane inequality.

Image with description On a coordinate plane, the x-axis labeled "x" ranges from negative 5 to 5 in increments of 1, and the y-axis labeled "y" ranges from negative 5 to 5 in increments of 1. The line passes through the quadrants 2, and 4 and through the points "negative 1 comma 3","0 comma 0" and "1 comma negative 3". Both ends of the line terminate with arrowheads at "negative 1 point 5 comma 5" and "1 point 5 comma negative 5". The entire region to the left of the line is shaded in a light tan color, representing a half-plane inequality.

Image with description On a coordinate plane, the x-axis labeled "x" ranges from negative 5 to 5 in increments of 1, and the y-axis labeled "y" ranges from negative 5 to 5 in increments of 1. A straight line is drawn passing through the points "negative 1 comma negative 3","0 comma 0" and "1 comma 3". Both ends of the line terminate with arrowheads at "1 point 5 comma 5" and "negative 1 point 5 comma negative 5". The entire region to the left of the line is shaded in a light tan color, representing a half-plane inequality.

Image with description On a coordinate plane, the x-axis labeled "x" ranges from negative 5 to 5 in increments of 1, and the y-axis labeled "y" ranges from negative 5 to 5 in increments of 1. A straight line is drawn passing through the points "negative 1 comma 3","0 comma 0" and "1 comma negative 3". Both ends of the line terminate with arrowheads at "negative 1 point 5 comma 5" and "1 point 5 comma negative 5". The entire region to the right of the line is shaded in a light tan color, representing a half-plane inequality.

Explanation

The boundary is the line y = -3x, which passes through (0, 0), (-1, 3), and (1, -3). Because the inequality includes equality (≤), the boundary line must be solid. The point (0, -1) satisfies the inequality, since -1 ≤ 0, and lies on the left side of this line; choice B has that side shaded.

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