Graphing Linear Inequalities in 2 Variables - Solid and Dotted

A linear inequality in two variables is an inequality that can be written in the form $$Ax + By < C$$ , $$Ax + By > C$$ , $$Ax + By \leq C$$ , or $$Ax + By \geq C$$ , where A, B, and C are constants.

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is either $$\leq$$ or $$\geq$$ .

A dotted line indicates that the points on the line are not included in the solution set, meaning the inequality is either $$<$$ or $$>$$ .

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

The slope-intercept form of a linear equation is $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

To convert a linear inequality to slope-intercept form, isolate $$y$$ on one side of the inequality.

The y-intercept is the point where the line crosses the y-axis, and it represents the value of $$y$$ when $$x = 0$$ .

$$y < mx + b$$ uses a dotted line, indicating that points on the line are not included, while $$y \leq mx + b$$ uses a solid line, indicating that points on the line are included.

1. Graph the corresponding linear equation as a solid or dotted line. 2. Choose a test point not on the line to determine which side of the line to shade.

A test point is a point used to determine which side of the line to shade. A common choice is the origin (0,0), unless it lies on the line.