4-4: Practice (Linear Inequalities)

Front

What does the inequality y ≥ -2x - 2 represent in terms of shading?

Back

The region above the line y = -2x - 2 will be shaded.

Front

What does the inequality y < x - 2 represent in terms of shading?

Back

The region below the line y = x - 2 will be shaded.

Front

Back

(0, 2) is in the solution set.

Front

What does the inequality y < 6x + 1 represent in terms of shading?

Back

The region below the line y = 6x + 1 will be shaded.

Front

Identify the graph for the linear inequality y < x - 2.

Back

The graph will show a dashed line for y = x - 2, with shading below the line.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function, typically expressed in the form ax + by < c, ax + by ≤ c, ax + by > c, or ax + by ≥ c.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Determine which side of the line to shade based on the inequality sign.

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 <).

Front

What does the solution set of an inequality represent?

Back

The solution set represents all the ordered pairs (x, y) that satisfy the inequality.

Front

How can you test if a point is in the solution set of an inequality?

Back

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