Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥). Then, shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The symbol '≤' indicates that the values of the variable can be less than or equal to the value on the other side of the inequality.

Tags

CCSS.6.EE.B.8

Front

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

Back

A dashed line indicates that points on the line are not included in the solution set (for strict inequalities), while a solid line indicates that points on the line are included (for inclusive inequalities).

Tags

CCSS.HSA.REI.D.12

Front

How can you determine which side of the line to shade when graphing a linear inequality?

Back

You can determine which side to shade by selecting a test point not on the line (commonly (0,0)) and substituting it into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

Tags

CCSS.HSA.REI.D.12

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

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

Back

To convert a linear inequality into slope-intercept form, isolate y on one side of the inequality, similar to how you would for an equation.

Front

What is the significance of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps to determine the starting point for graphing the line.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean for a solution to be 'bounded' in the context of linear inequalities?

Back

A solution is 'bounded' if it is restricted to a certain range of values, meaning there are limits on how far the values can go in either direction.

Front

What are the key characteristics of a linear inequality graph?

Back

Key characteristics include a straight line (either dashed or solid), a shaded region indicating the solution set, and the direction of the shading based on the inequality.

Tags

CCSS.HSA.REI.D.12