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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to a certain number.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (if ≥ or ≤) or a dashed line (if > 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 inequality 'y < mx + b' represent?

Back

It represents the region below the line defined by the equation y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

What does the inequality 'y ≥ mx + b' represent?

Back

It represents the region above the line defined by the equation y = mx + b, 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)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

What does the slope 'm' indicate in a linear inequality?

Back

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

Front

What is the y-intercept 'b' in a linear equation?

Back

The y-intercept 'b' is the point where the line crosses the y-axis, represented as (0, b).