Linear Inequalities Quiz

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Questions and Answers

What is the symbol used for inequalities?

≤ or ≥

What type of inequalities are represented by a dashed line when graphing?

  • Non-strict inequalities
  • Strict inequalities (correct)

What are the symbols for 'less than or equal to' and 'greater than or equal to'?

  • < and >
  • ≤ and ≥ (correct)

Flashcards

Inequality

A mathematical statement comparing two expressions using symbols like <, >, ≤, or ≥.

Ordered Pair

A pair of numbers (x, y) that represents a point on a coordinate plane.

Slope-Intercept Form

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

Dashed Line

A line used to graph inequalities with < or >. It means the points on the line are not part of the solution.

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Solid Line

A line used to graph inequalities with ≤ or ≥. It means the points on the line are part of the solution.

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Linear Inequality

An inequality that involves a linear equation.

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Solve an Inequality

To find the solution set of values that satisfy the inequality.

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Convert to Slope-Intercept Form

Rewrite an inequality in the form y = mx + c.

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Graph an Inequality

Represent the solution set of an inequality on a coordinate plane.

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Testing a Point

Substituting coordinates of a point not on the line into the original inequality.

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Solution Set

The set of all ordered pairs that satisfy the inequality.

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Slope

The rate of change of y with respect to x.

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y-intercept

The point where the line crosses the y-axis.

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Verify a solution

Check if a given ordered pair makes the inequality true.

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Graphing Linear Inequalities

Method for plotting linear inequalities on coordinate plane, involving slope-intercept form and determining the shaded region.

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Inequality Symbols

Symbols used to compare expressions (<, >, ≤, ≥).

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Solution to an inequality

Value(s) of a variable that satisfy the inequality.

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Half-plane

The two regions on either side of a line in a coordinate plane

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Linear equation

An equation whose graph is a straight line

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Study Notes

Linear Inequalities

  • Linear inequalities are similar to linear equations but use inequality symbols
  • The solution to a linear inequality involves finding all ordered pairs that make the inequality true
  • Example: 2x - 3y < 15
  • To graph a linear inequality:
    • Convert the inequality to slope-intercept form (y = mx + b)
    • Determine if the line should be solid or dashed (solid for ≤ or ≥, dashed for < or >)
    • Choose a test point (not on the line) to determine which side of the line to shade. If the test point satisfies the inequality, shade that side; otherwise, shade the other side.
  • If the inequality is multiplied or divided by a negative number, flip the inequality sign

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