Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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 an inequality?

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the number.

Front

What does the symbol '≤' mean in an inequality?

Back

'≤' means 'less than or equal to', indicating that the value can be either less than or equal to the number.

Front

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

Back

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

Front

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

Back

Choose a test point not on the line (commonly (0,0)). Substitute 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

Front

How do you convert a linear equation to an inequality?

Back

To convert a linear equation to an inequality, replace the '=' sign with an inequality symbol (>, <, ≥, ≤) based on the context of the problem.

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 in plotting the line for the corresponding linear equation.

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 is included in the solution set if the line is solid (≥ or ≤) and excluded if the line is dashed (> or <).