Graphing Linear Inequality

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 ≥). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

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

Front

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

Back

'≤' means 'less than or equal to'. It 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 does the symbol '≥' mean in a linear inequality?

Back

'≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to the value on the other side of the inequality.

Front

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

Back

Front

How do you find the slope of a line from a linear inequality?

Back

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis. It helps in graphing the inequality and understanding the relationship between the variables.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it satisfies the equation of the line. Depending on the inequality, it may or may not be included in the solution set.

Front

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

Back

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

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.