Graphing Linear Inequality

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 solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the points where the inequality changes from true to false. Points on the line are included if the inequality is ≤ or ≥.

Front

What does it mean if a point is part of the solution set?

Back

It means that the point satisfies the inequality when substituted into it.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) does include the boundary line.

Front

How can you determine if a point is in the solution set of a linear inequality?

Back

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

Front

What does the inequality y > -x - 5 represent graphically?

Back

It represents the region above the line y = -x - 5, excluding the line itself.

Front

What is the role of test points in graphing linear inequalities?

Back

Test points help determine which side of the boundary line to shade. If the test point satisfies the inequality, shade that side.

Front

Can a linear inequality have multiple solutions?

Back

Yes, a linear inequality can have infinitely many solutions, represented by the shaded region on the graph.