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 the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

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

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

You can test a point not on the line (usually (0,0) if it's not on the line) in the inequality. If the inequality holds true, shade the side containing that point.

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 convert a linear inequality to slope-intercept form?

Back

Isolate y on one side of the inequality to express it in the form y < mx + b or y > mx + b.

Front

What does the term 'boundary line' refer to in graphing inequalities?

Back

The boundary line is the line that represents the equation of the inequality, separating the solution set from non-solution set.

Front

What is the significance of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis, providing a starting point for graphing the line.

Front

How do you identify the solution set of a linear inequality from its graph?

Back

The solution set is represented by the shaded region of the graph, which includes all points (x, y) that satisfy the inequality.