Flashcard 4.3-4.4 Linear Inequalities and System of Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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What does the solution of a linear inequality represent?

Back

The solution of a linear inequality represents all the values that satisfy the inequality, often visualized as a region on a graph.

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How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality.

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 they are not included (> or <).

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables, and the solution is the region where all inequalities overlap.

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How do you find the solution to a system of inequalities?

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To find the solution to a system of inequalities, graph each inequality and identify the overlapping shaded region.

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What does the point (2,1) represent in the context of linear inequalities?

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The point (2,1) is a solution to a linear inequality if it satisfies the inequality when substituted into it.

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What is the significance of the y-intercept in a linear inequality?

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The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality.

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How do you determine if a point is a solution to a linear inequality?

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To determine if a point is a solution, substitute the x and y values into the inequality and check if the statement is true.