Graphing Inequalities

Front

What does it mean when a graph has a dashed line?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

Front

What does it mean when a graph has a solid line?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

Front

How do you determine the shading direction for the inequality y > mx + b?

Back

If the inequality is 'greater than' (>) the shading is above the line; if it is 'less than' (<), the shading is below the line.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all points (x, y) that satisfy the inequality.

Front

How do you graph the inequality y < 2x + 1?

Back

1. Graph the line y = 2x + 1 with a dashed line. 2. Shade below the line.

Front

What is the difference between y > mx + b and y ≥ mx + b?

Back

y > mx + b uses a dashed line and shades above, while y ≥ mx + b uses a solid line and shades above.

Front

Which point is part of the solution set for y < -x + 2?

Back

To determine if a point is part of the solution set, substitute the point into the inequality. For example, (1, 0) gives 0 < -1 + 2, which is true.

Front

What does the inequality x < -3 represent on a graph?

Back

It represents a vertical line at x = -3 with a dashed line, shading to the left.

Front

How do you identify the correct graph for the inequality y ≥ -2x - 3?

Back

Graph the line y = -2x - 3 with a solid line and shade above the line.

Front

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

Back

The slope (m) indicates the steepness and direction of the line; a positive slope rises to the right, while a negative slope falls to the right.