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 in two variables?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Shade the region that satisfies the inequality.

Front

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

Back

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

Front

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

Back

It represents the region above the line y = 2x + 3, not including the line itself.

Front

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

Back

Choose a test point not on the line (commonly (0,0)). If the inequality holds true for that point, shade the side containing the 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

What does the slope of a line indicate in a linear inequality?

Back

The slope indicates the steepness and direction of the line; a positive slope rises from left to right, while a negative slope falls.

Front

What is the y-intercept in the equation y ≤ 2/5x + 1?

Back

The y-intercept is 1, which is the point where the line crosses the y-axis.

Front

How can you convert a linear inequality into slope-intercept form?

Back

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