Graphing Linear Inequalities

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 symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the values satisfying the inequality can be equal to or greater than the given expression.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dotted line (for > or <). 2. Shade the appropriate region (above or below the line) based on the inequality.

Front

What does it mean if a line is solid in a graph of a linear inequality?

Back

A solid line indicates that points on the line are included in the solution set (for inequalities with ≥ or ≤).

Front

What does it mean if a line is dotted in a graph of a linear inequality?

Back

A dotted line indicates that points on the line are not included in the solution set (for inequalities with > or <).

Front

How do you determine which side of the line to shade in a linear inequality?

Back

To determine which side to shade, pick a test point (often (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the y-intercept of the line y = -2x + 1?

Back

The y-intercept is the point where the line crosses the y-axis, which occurs at (0, 1).

Front

What is the slope of the line represented by the inequality y ≥ -2x + 1?

Back

The slope is -2, indicating that for every 1 unit increase in x, y decreases by 2 units.

Front

What does the solution set of a linear inequality represent?

Back

The solution set represents all the points (x, y) that satisfy the inequality, which can be visualized as a shaded region on the graph.

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.