Intro to 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?

Back

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

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality, indicating the set of points that satisfy the inequality.

Front

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

Back

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

Front

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

Back

To determine if a point is a solution, 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 typically written as Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

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

Back

The symbol '>' means 'greater than' and indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

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

Back

The symbol '<' means 'less than' and indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What is an ordered pair in the context of inequalities?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on the Cartesian plane, where 'x' is the horizontal coordinate and 'y' is the vertical coordinate.

Front

How do you identify the boundary line of a linear inequality?

Back

The boundary line of a linear inequality can be identified by rewriting the inequality as an equation (e.g., y = mx + b) and graphing it.