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

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

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Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

Problem 12

Chapter 6, Problem 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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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.