Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

검증된 단계별 안내

Identify the inequality given: \(y \leq -3x - 6\). This represents all points on or below the line \(y = -3x - 6\).

Rewrite the boundary line equation: \(y = -3x - 6\). This line has a slope of \(-3\) and a y-intercept at \(-6\).

Determine the shading region for the inequality \(y \leq -3x - 6\). Since it is \(\leq\), the solution includes the line and the area below it.

On each graph option (A–D), look for the line with slope \(-3\) and y-intercept \(-6\), then check which graph shades the region below this line.

Match the inequality \(y \leq -3x - 6\) to the graph that shows the line \(y = -3x - 6\) with shading below or on the line.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Graphing Linear Inequalities

Graphing a linear inequality involves first graphing the related linear equation as a boundary line. The inequality symbol determines whether the boundary is solid (≤ or ≥) or dashed (< or >). The solution region is the half-plane where the inequality holds true, shaded accordingly.

Slope-Intercept Form

The slope-intercept form y = mx + b expresses a line with slope m and y-intercept b. For y ≤ -3x - 6, the slope is -3, indicating the line falls steeply, and the y-intercept is -6, where the line crosses the y-axis. This form helps quickly sketch the boundary line.

Testing Points to Determine Shading

To identify which side of the boundary line to shade, select a test point not on the line (often (0,0)) and substitute into the inequality. If the inequality is true, shade the region containing that point; if false, shade the opposite side. This confirms the correct solution region.