Graphing Inequalities Practice

Front

What is the general form of a linear inequality?

Back

A linear inequality can be expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.

Front

How do you determine if a line is solid or dashed when graphing an inequality?

Back

A solid line is used when the inequality includes 'or equal to' (≤ or ≥), while a dashed line is used when it does not ( < or >).

Front

What does the inequality y < -4x - 1 represent graphically?

Back

It represents the region below the line y = -4x - 1, where all points (x, y) satisfy the inequality.

Front

What is the significance of the slope in the inequality y ≤ (2/5)x + 1?

Back

The slope (2/5) indicates the steepness of the line, showing that for every 5 units moved horizontally, the line moves 2 units vertically.

Front

What does the inequality y ≥ -2x + 1 indicate about the shading of the graph?

Back

The graph is shaded above the line y = -2x + 1, indicating that all points above this line satisfy the inequality.

Front

How do you graph the inequality y < -4x - 1?

Back

First, graph the line y = -4x - 1 as a dashed line, then shade the area below the line.

Front

What is the meaning of the inequality symbol '≤'?

Back

The symbol '≤' means 'less than or equal to', indicating that the values on the line are included in the solution set.

Front

What does the inequality y ≥ -5/4x + 3 represent?

Back

It represents the region above the line y = -5/4x + 3, including the line itself, where all points (x, y) satisfy the inequality.

Front

How can you tell if a point (x, y) is a solution to the inequality y < -4x - 1?

Back

Substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) do include the boundary line.