Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Front

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

Back

Front

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

Back

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

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as if it were an equality. 2. Use a solid or dashed line based on the inequality. 3. Shade the appropriate region to represent the solution set.

Front

What does it mean to shade above the line in a graph of an inequality?

Back

Shading above the line indicates that the solution includes all points where the y-value is greater than the line (for inequalities like y > mx + b or y ≥ mx + b).

Front

What does it mean to shade below the line in a graph of an inequality?

Back

Shading below the line indicates that the solution includes all points where the y-value is less than the line (for inequalities like y < mx + b or y ≤ mx + b).

Front

What is the y-intercept of a line?

Back

Front

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

Back

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