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

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for ).

How can you convert a linear inequality into slope-intercept form?

To convert a linear inequality into slope-intercept form, isolate y on one side of the inequality. For example, from $$y

What does it mean if a graph of a linear inequality is shaded above the line?

If the graph is shaded above the line, it indicates that the inequality is of the form $$y > mx + b$$ or $$y \\geq mx + b$$ , meaning y values are greater than the corresponding x values on the line.

What does it mean if a graph of a linear inequality is shaded below the line?

If the graph is shaded below the line, it indicates that the inequality is of the form $$y

How do you write a linear inequality from a graph?

To write a linear inequality from a graph, identify the slope and y-intercept of the boundary line, determine if the line is solid or dashed, and decide whether to shade above or below the line based on the direction of the inequality.

What is the slope of the line represented by the inequality $$y \\leq -\frac{3}{5}(x - 3) + 2$$ ?

The slope of the line is $$-\frac{3}{5}$$ .

What is the y-intercept of the line represented by the inequality $$y \\leq -\frac{3}{5}(x - 3) + 2$$ ?

To find the y-intercept, set $$x = 0$$ in the equation. The y-intercept is $$y = -\frac{3}{5}(0 - 3) + 2 = \frac{11}{5}$$ .

How do you interpret the solution of a linear inequality graphically?

Graphically, the solution of a linear inequality is represented by the shaded region of the graph, which includes all the points that satisfy the inequality.

Linear inequalities (two variables) 12.3.24

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA.REI.D.12

Standards-aligned

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FLASHCARD QUESTION

Front

What is a linear inequality in two variables?

Back

FLASHCARD QUESTION

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the values of the variable can be equal to the boundary line or less than it.

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the values of the variable can be equal to the boundary line or greater than it.

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false. It divides the graph into two regions: one that satisfies the inequality and one that does not.

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

How do you determine which side of the boundary line to shade?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Tags

CCSS.HSA.REI.D.12

FLASHCARD QUESTION

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region on the graph.

Tags

CCSS.HSA.REI.D.12

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