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.

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.

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).

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.

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.

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.

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.