How do you graph the inequality $$y \leq \frac{1}{2}x + 2$$ ?

To graph $$y \leq \frac{1}{2}x + 2$$ , first graph the line $$y = \frac{1}{2}x + 2$$ as a solid line (since it includes equality). Then shade below the line to represent all points where $$y$$ is less than or equal to the line.

What does the symbol $$y > -3x - 1$$ represent?

The symbol $$y > -3x - 1$$ represents all points above the line $$y = -3x - 1$$ , which is a dashed line indicating that points on the line are not included in the solution.

How do you graph the inequality $$2x - y > 4$$ ?

To graph $$2x - y > 4$$ , first graph the line $$2x - y = 4$$ as a dashed line. Then shade above the line to represent all points where $$2x - y$$ is greater than 4.

What is the significance of the intersection of two shaded regions in a graph of inequalities?

The intersection of two shaded regions represents the solution set where both inequalities are satisfied.

What does the inequality $$y \leq 3x$$ represent graphically?

The inequality $$y \leq 3x$$ represents all points on or below the line $$y = 3x$$ .

How can you tell if a point is a solution to the inequality $$y > 3x$$ ?

To check if a point is a solution to $$y > 3x$$ , substitute the x-coordinate into the inequality and see if the y-coordinate is greater than the result.

What is the purpose of graphing systems of inequalities?

Graphing systems of inequalities helps visualize the solution set and understand the relationships between different inequalities.

What does it mean if a point lies outside the shaded region of a graph of inequalities?

If a point lies outside the shaded region, it means that the point does not satisfy at least one of the inequalities in the system.

How do you identify the correct region that represents the solution set?

To identify the correct region, graph each inequality, shade the appropriate areas, and find the overlapping region that satisfies all inequalities.

What is the role of the boundary line in graphing inequalities?

The boundary line separates the graph into regions and helps determine where the inequality holds true.

Graphing Systems of Inequalities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.D.12

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.D.12

4.

FLASHCARD QUESTION

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the region on the graph where all inequalities are satisfied simultaneously.

Tags

CCSS.HSA.REI.D.12

5.

FLASHCARD QUESTION

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

6.

FLASHCARD QUESTION

Front

What does it mean if a region is shaded in a graph of inequalities?

Back

Shaded regions in a graph of inequalities indicate the set of all possible solutions that satisfy the inequalities.

Tags

CCSS.HSA.REI.D.12

7.

FLASHCARD QUESTION

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

Tags

CCSS.HSA.REI.D.12

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