4-4 Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality symbol is ≤ or ≥.

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, which occurs when the inequality symbol is < or >.

Front

How do you determine the slope from the equation of a line?

Back

The slope (m) can be determined from the equation in the form y = mx + b, where m is the coefficient of x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented in the equation as y = mx + b.

Front

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

Back

Graph the line y = 2x + 1 with a dashed line, then shade above the line to represent all points where y is greater than 2x + 1.

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 can you check 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 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) does not include the boundary point, while 'greater than or equal to' (≥) includes the boundary point.

Front

How do you write an inequality from a word problem?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using inequality symbols.