Linear Inequalities TWO Variables

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What is a linear inequality in two variables?

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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. Use a dashed line for < or >, and a solid line for \leq or \geq. Then, shade the region that satisfies the inequality.

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What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality, forming a region on the graph.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (\leq or \geq) includes the boundary line.

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

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What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the solution set from the non-solution set. Points on the line are included if the inequality is non-strict.

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How do you identify the correct inequality from a graph?

Back

Look at the slope and y-intercept of the boundary line, and determine if the region is shaded above or below the line to identify the correct inequality.

Front

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

Back

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