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 symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed line (for < or >) or a solid 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

What does the solution set of a linear inequality represent?

Back

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

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 test point satisfies the inequality, shade the region 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.

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, indicating the value of y when x = 0.