[W3/D2] 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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, which is the region of the coordinate plane that satisfies the inequality.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Use a dashed line for < or > (not including the line) and a solid line for ≤ or ≥ (including the line). 3. Shade the region that satisfies the inequality.

Front

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

Back

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

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Front

How do you determine which side of the line to shade when graphing an inequality?

Back

Choose a test point not on the line (commonly (0,0)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side of the line that includes the test point; otherwise, shade the opposite side.

Front

What is the significance of the slope in a linear inequality?

Back

The slope (m) indicates the steepness and direction of the line. A positive slope means the line rises from left to right, while a negative slope means it falls.

Front

What does the y-intercept represent in a linear inequality?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x = 0.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region.