4.4 Inequalities of Two Variables

Front

What is an inequality in two variables?

Back

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) and involves two variables, typically x and y.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions that satisfy the inequality, often shaded to indicate the region of valid solutions.

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

Front

Back

You shade below the line because the inequality is less than (<).

Front

What is the slope-intercept form of a linear equation?

Back

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Back

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Front

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the significance of the boundary line in an inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it may or may not be included in the solution set, depending on whether the inequality is strict or non-strict.