Graphs of Linear Inequalities and Absolute Value

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 or solid line, then shade the region that satisfies the inequality.

Front

What does the absolute value function represent?

Back

The absolute value function represents the distance of a number from zero on the number line, regardless of direction.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = |x - h| + k, where (h, k) is the vertex of the graph.

Front

How does the graph of f(x) = |x| change when you add a constant?

Back

Adding a constant shifts the graph vertically. For example, f(x) = |x| + 3 shifts the graph up by 3 units.

Front

What effect does a negative sign have in front of an absolute value function?

Back

A negative sign reflects the graph of the absolute value function across the x-axis.

Front

What does the vertex of an absolute value graph represent?

Back

The vertex represents the minimum or maximum point of the graph, depending on the direction it opens.

Front

How do you determine the direction of shading for a linear inequality?

Back

The direction of shading is determined by the inequality symbol: use a solid line for ≥ or ≤ and a dashed line for > or <.

Front

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

Back

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

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side using inverse operations, similar to solving an equation.