Graphing Two-Variable Linear Inequalities

Study Notes

Graphing Two-Variable Linear Inequalities

Understanding of linear inequalities can be enhanced through graphical representation, showing which areas of the graph contain solutions.

Inequality Representations

The graph of a linear inequality can represent different forms based on its slope and intercepts.
Example: For the inequality y < 2/3 x + 3, the area below the line is shaded.

Solution Points

Not all points will satisfy an inequality; specific points can be checked against the inequality to confirm if they are solutions.
Example: For y < 0.5x + 2, valid solution points include (-3, -2), (-1, -2), (1, -2), and (1, 2).

Graphing Techniques

Graphs may indicate whether the inequality is strict (open circles) or inclusive (closed circles), guiding whether the boundary line is part of the solution set.

Inequality Form Examples

y > −3x + 2 suggests shading above the line; points satisfying this include (2, 0).
Inequalities such as 2x - 3y < 12 require correct graphing to determine feasible solutions visually.

Interpretation of Graphs

Each graph representation varies with the slope-intercept format, where the coefficient of x directly influences the line's steepness.
Identifying the correct inequality form is crucial when corresponding to a graph’s linearity.

Key Points to Remember

When determining solutions, checking multiple points against the inequality is essential for accuracy.
Recognize that shading indicates the area where all potential solutions to the inequality reside in relation to the boundary line.

Description

Test your knowledge of graphing linear inequalities with this flashcard quiz. Determine which inequalities correspond to given graphs and identify solution points accurately. Perfect for visual learners and mathematics students!