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 a linear inequality?

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the specified number.

Front

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

Back

'≤' means 'less than or equal to', indicating that the value can be either less than or equal to the specified number.

Front

How do you graph a linear inequality?

Back

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

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 if a point is a solution to a linear inequality?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all points (x, y) that satisfy the inequality.

Front

What does it mean to shade above a line in a graph?

Back

Shading above a line indicates that the solution set includes all points above the line, typically used for inequalities like y > mx + b.

Front

What does it mean to shade below a line in a graph?

Back

Shading below a line indicates that the solution set includes all points below the line, typically used for inequalities like y < mx + b.

Front

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

Back

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