Graphing Linear Inequalities Flashcard

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 solid line (for ≥ or ≤) or a dashed line (for > or <). Then shade the appropriate region based on the inequality.

Front

What does it mean if a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (for ≥ or ≤).

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (for > or <).

Front

How do you determine which side of the line to shade in a graph of an inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)). If the test point satisfies the inequality, shade the side containing that point.

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.

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. A positive slope means the line rises, while a negative slope means it falls.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the slope and y-intercept of the line, and determine the direction of the shading to establish the inequality.

Front

What is the y-intercept in the inequality y < 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

What does the inequality y > 7/3x + 2 represent graphically?

Back

It represents a region above the line with a slope of 7/3 and a y-intercept of 2.