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 convert a linear inequality to slope-intercept form?

Back

To convert a linear inequality to slope-intercept form (y = mx + b), isolate y on one side of the inequality.

Front

What does the slope-intercept form of a linear inequality represent?

Back

The slope-intercept form of a linear inequality represents a line on a graph, where the slope (m) indicates the steepness and the y-intercept (b) indicates where the line crosses the y-axis.

Front

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

Back

The inequality symbol indicates the relationship between the two sides of the inequality, determining whether the solution set includes points above or below the line.

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 appropriate region based on the inequality symbol.

Front

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

Back

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

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality, typically shown as a shaded region on a graph.

Front

How can you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)), substitute it into the inequality, and shade the side that makes the inequality true.

Front

What is the slope of the line represented by the inequality y < -3/5x + 1?

Back

The slope of the line is -3/5.

Front

What does the y-intercept represent in the inequality y ≥ -3/4x + 3?

Back

The y-intercept represents the point where the line crosses the y-axis, which is (0, 3) in this case.