Graphing Linear Inequalites

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

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

Back

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

Front

How do you determine the boundary line for a linear inequality?

Back

To determine the boundary line, convert the inequality to an equation (replace the inequality sign with an equals sign) and graph that line.

Front

What does the shaded region in the graph of a linear inequality indicate?

Back

The shaded region indicates all the possible solutions to the inequality, showing where the inequality holds true.

Front

How do you graph the inequality y < 2x + 3?

Back

First, graph the line y = 2x + 3 with a dotted line, then shade below the line to represent all points where y is less than 2x + 3.

Front

What is the significance of the inequality symbol in graphing?

Back

The inequality symbol determines whether the boundary line is solid or dotted and indicates which side of the line to shade.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

Front

How can you check if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

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.