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 it mean when a graph is shaded above the line?

Back

It indicates that the solutions to the inequality are all the points above the line, meaning the y-values are greater than the values on the line.

Front

What does it mean when a graph is shaded below the line?

Back

It indicates that the solutions to the inequality are all the points below the line, meaning the y-values are less than the values on the line.

Front

How do you determine if the line is solid or dashed in a graph of an inequality?

Back

A solid line indicates that the inequality includes the boundary (≥ or ≤), while a dashed line indicates it does not include the boundary (> or <).

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph the inequality y ≥ 2x + 1?

Back

First, graph the line y = 2x + 1 as a solid line, then shade above the line to represent y-values greater than or equal to the line.

Front

What does the inequality x < -1 represent on a number line?

Back

It represents all numbers to the left of -1, not including -1 itself.

Front

What is the significance of flipping the inequality sign?

Back

The inequality sign must be flipped when multiplying or dividing both sides of the inequality by a negative number.

Front

How do you write an inequality from a graph?

Back

Identify the slope and y-intercept of the line, determine if the line is solid or dashed, and decide whether to shade above or below the line.

Front

What is the solution set of the inequality y < 3x - 2?

Back

The solution set includes all points below the line y = 3x - 2.