7.3 Writing Inequalities from Graphs

Front

What is an inequality?

Back

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

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

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

Back

A solid line indicates that points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you determine the shading direction in a graph of an inequality?

Back

Shading is determined by the inequality sign: shade above the line for '≥' or '>' and below the line for '≤' or '<'.

Front

What does the inequality y ≤ 2/5x + 1 represent graphically?

Back

It represents a region below or on the line y = 2/5x + 1, including the line itself.

Front

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

Back

It represents a region above or on the line y = -5/4x + 3, including the line itself.

Front

What is a boundary line in the context of inequalities?

Back

A boundary line is the line that represents the equation of the inequality, separating the solution set from non-solution set.

Front

Are points on the boundary line included in the solution set for '≥' or '≤' inequalities?

Back

Yes, points on the boundary line are included in the solution set for '≥' or '≤' inequalities.

Front

What is the solution set of an inequality?

Back

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