Graphing Solutions to Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical expression that shows the relationship between two variables using an inequality sign (such as <, >, ≤, or ≥) instead of an equal sign.

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How do you represent a real-world situation with a linear inequality?

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To represent a real-world situation with a linear inequality, identify the variables, determine the relationship between them, and express it using an inequality that reflects the constraints of the situation.

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What does the symbol '≥' mean in a linear inequality?

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The symbol '≥' means 'greater than or equal to', indicating that the value on the left side of the inequality is either greater than or equal to the value on the right side.

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

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The slope in a linear inequality graph indicates the rate of change between the two variables. It determines the steepness of the line and the direction of the inequality.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥). Then, shade the appropriate region that satisfies the inequality.

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What does it mean for a point to be a solution to a linear inequality?

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A point is a solution to a linear inequality if it satisfies the inequality when the coordinates of the point are substituted into the inequality.

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How can 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 coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

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What is the difference between a linear equation and a linear inequality?

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A linear equation shows an exact relationship between variables and has a solution that forms a straight line, while a linear inequality shows a range of possible solutions and represents a region on a graph.

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What is the standard form of a linear inequality?

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The standard form of a linear inequality is typically written as Ax + By < C, Ax + By ≤ C, Ax + By > C, or Ax + By ≥ C, where A, B, and C are constants.

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How do you convert a word problem into a linear inequality?

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To convert a word problem into a linear inequality, identify the quantities involved, define the variables, and translate the relationships and constraints described in the problem into an inequality.