Inequality Systems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does a dashed line represent in an inequality graph?

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 a solid line represent in an inequality graph?

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 graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 with a dashed line, and shade below the line to represent all points where y is less than 2x + 3.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you determine 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.

Front

What is the difference between 'y ≤ mx + b' and 'y < mx + b'?

Back

'y ≤ mx + b' includes the line (solid line), while 'y < mx + b' does not include the line (dashed line).

Front

What does the slope of a line in an inequality represent?

Back

The slope (m) represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept in the equation of a line?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Front

How do you write an inequality from a graph?

Back

Identify the slope and y-intercept, determine if the line is solid or dashed, and decide whether to shade above or below the line based on the direction of the inequality.