Graph each inequality. y\u003e−3

Identify the inequality given: $$y \u003e -3. $$This means we are looking for all points where the y-coordinate is greater than -3. Graph the boundary line $$y = -3. $$Since the inequality is strict (greater than, not greater than or equal to), draw this line as a dashed horizontal line to indicate that points on the line are not included. Determine which side of the line to shade. Since the inequality is $$y \u003e -3$$, shade the region above the line $$y = -3$$ because those points have y-values greater than -3. Check a test point not on the boundary line to confirm the shading. For example, use the point $$(0,0)$$: since $$0 \u003e -3 is $$true, the region containing $$(0,0)$$ should be shaded. Label the graph clearly with the dashed line at $$y = -3$$ and the shaded region above it to represent all solutions to the inequality $$y \u003e -3.$$

Ch. 5 - Systems of Equations and Inequalities

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Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

Problema 12

Capitolo 6, Problema 12

Graph each inequality. y>−3

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Identify the inequality given: $y > -3$. This means we are looking for all points where the y-coordinate is greater than -3.

Graph the boundary line $y = -3$. Since the inequality is strict (greater than, not greater than or equal to), draw this line as a dashed horizontal line to indicate that points on the line are not included.

Determine which side of the line to shade. Since the inequality is $y > -3$, shade the region above the line $y = -3$ because those points have y-values greater than -3.

Check a test point not on the boundary line to confirm the shading. For example, use the point $(0,0)$: since $0 > -3$ is true, the region containing $(0,0)$ should be shaded.

Label the graph clearly with the dashed line at $y = -3$ and the shaded region above it to represent all solutions to the inequality $y > -3$.

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Graphing Linear Inequalities

Graphing linear inequalities involves shading a region of the coordinate plane that satisfies the inequality. For an inequality like y > -3, you first graph the boundary line y = -3, then determine which side of the line to shade based on the inequality symbol.

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Linear Inequalities

Boundary Lines and Their Types

The boundary line for an inequality is drawn as either solid or dashed. A solid line is used for ≤ or ≥ inequalities, indicating points on the line are included. A dashed line is used for < or > inequalities, indicating points on the line are not included in the solution.

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Types of Slope

Testing Points to Determine Shading

To decide which side of the boundary line to shade, select a test point not on the line (often (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

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Determinants of 2×2 Matrices

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