Graphing Inequalities

Front

What does the inequality x ≥ -5 represent on a number line?

Back

The graph includes all numbers greater than or equal to -5, with a solid dot at -5 and a line extending to the right.

Front

How do you represent the inequality x < 6 on a number line?

Back

The graph includes all numbers less than 6, with a dashed line approaching 6 and extending to the left.

Front

What type of line is used to represent the inequalities < and >?

Back

A dashed or dotted line is used to indicate that the endpoints are not included in the solution set.

Front

What does the inequality y > 3/4x + 5 indicate about the graph?

Back

The area above the line y = 3/4x + 5 is shaded, indicating that y values greater than the line are included.

Front

How do you graph the inequality b ≤ -2?

Back

The graph includes all values less than or equal to -2, with a solid dot at -2 and a line extending to the left.

Front

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

Back

A solid line indicates that the endpoint is included (≥ or ≤), while a dashed line indicates that the endpoint is not included (< or >).

Front

How do you determine the solution set for the inequality y < 2x - 3?

Back

Graph the line y = 2x - 3 with a dashed line and shade below the line to represent all y values less than the line.

Front

What does the inequality x > 4 mean in terms of a number line?

Back

The graph includes all numbers greater than 4, with a dashed line approaching 4 and extending to the right.

Front

How can you tell if an inequality is represented correctly on a graph?

Back

Check if the shaded region corresponds to the inequality and if the line type (solid or dashed) matches the inequality symbols.

Front

What is the significance of the slope in the inequality y < mx + b?

Back

The slope (m) indicates the steepness of the line, affecting the direction of the shading based on the inequality.