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

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

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

Back

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

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 as a shaded region on the coordinate plane.

Front

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

Back

To determine which side to shade, pick 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; if false, shade the opposite side.

Front

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

Back

Front

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

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 x and y.