Linear Inequalities in Two Variables

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What is a linear inequality in two variables?

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What does the graph of a linear inequality represent?

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The graph of a linear inequality represents a region in the coordinate plane that includes all the solutions to the inequality.

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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 (x, y) is a solution to a linear inequality, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

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What is the difference between '<' and '≤' in linear inequalities?

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The symbol '<' indicates that the boundary line is not included in the solution set (dashed line), while '≤' indicates that the boundary line is included (solid line).

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What is the significance of the slope in a linear inequality?

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The slope of the line in a linear inequality indicates the steepness and direction of the line, which helps in determining the region that satisfies the inequality.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Choose a test point not on the line (usually (0,0)). 3. Substitute the test point into the inequality. If true, shade the region containing the test point; if false, shade the opposite region.

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What does the term 'boundary line' refer to in linear inequalities?

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The boundary line is the line that represents the equation of the linear inequality. It divides the coordinate plane into two half-planes.

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What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the graph.

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What is the role of the y-intercept in graphing linear inequalities?

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The y-intercept is the point where the line crosses the y-axis, and it is used to plot the line when graphing the corresponding linear equation.

Front

How can you convert a linear inequality into slope-intercept form?

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