Graphing Linear Inequalities (S4Q4 Alg I Review)

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 (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

Front

What does the symbol '≥' mean in an inequality?

Back

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

Front

What does the symbol '≤' mean in an inequality?

Back

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

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 '>' and '≥'?

Back

'>' means strictly greater than, while '≥' means greater than or equal to. The former does not include the boundary, while the latter does.

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. It is represented graphically as a shaded region on the coordinate plane.

Front

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

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

Front

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

Back

Front

How do you convert a linear equation to an inequality?

Back

To convert a linear equation to an inequality, replace the equality sign '=' with an inequality symbol (<, >, ≤, or ≥) based on the context of the problem.

Front

What does it mean if a linear inequality has no solution?

Back

A linear inequality has no solution if the shaded regions do not overlap, indicating that there are no points that satisfy the inequality.