Systems of Linear Inequalities (A1.1.3.2.1, A1.1.3.2.2) FL

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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

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

Back

The symbol '>' indicates that the values of the variable are greater than the value on the other side of the inequality.

Front

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

Back

The symbol '<' indicates that the values of the variable are less than the value on the other side of the inequality.

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 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line and indicates that points on the line are not included, while 'y ≤ mx + b' uses a solid line and includes points on the line.

Front

What does the solution to a system of linear inequalities represent?

Back

The solution to a system of linear inequalities represents the set of all points that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

Front

What is the significance of the intersection of shaded regions in a graph of linear inequalities?

Back

The intersection of shaded regions represents the solution set that satisfies all inequalities in the system.

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What is the role of the slope in a linear inequality?

Back

The slope (m) indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises, while a negative slope means it falls.