Graphing Linear Inequalities

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

1. Graph the corresponding linear equation as a solid or dashed line. 2. Shade the region that satisfies the inequality.

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

The slope of a line is a measure of its steepness, calculated as the ratio of the rise (vertical change) to the run (horizontal change), expressed as $$\frac{rise}{run}$$ .

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

It represents all numbers to the left of -1, not including -1 itself.

The solution set includes all points (x, y) that lie on or below the line represented by the equation y = 5x - 1.

The equal sign indicates that the boundary line is included in the solution set, resulting in a solid line.