Special Cases

Learn and apply special cases using equations, examples, and interpretation.

Lesson 4 of 53 parts Practice Flashcards

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Parallel Lines

Objective: Explain and use parallel lines in an Algebra 1 problem.

Distinct parallel lines have no intersection, so the corresponding system has no solution. A contradiction such as 0=5.

Worked examples

Try itExample 1.1: How many intersections do y=4x+17 and y=4x+18 have?Show answer

0. Equal slopes with different intercepts describe parallel lines. The answer is 0.

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Parallel Lines

Objective: Explain and use parallel lines in an Algebra 1 problem.

Distinct parallel lines have no intersection, so the corresponding system has no solution. A contradiction such as 0=5.

Worked examples

Try itExample 1.1: How many intersections do y=4x+17 and y=4x+18 have?Show answer

0. Equal slopes with different intercepts describe parallel lines. The answer is 0.

Coincident Lines

Objective: Explain and use coincident lines in an Algebra 1 problem.

Equivalent equations graph as one line; every point on it is a solution, giving infinitely many solutions. An identity such as 0=0.

Worked examples

Try itExample 2.1: How many intersections do y=2x+27 and y=2x+28 have?Show answer

0. Equal slopes with different intercepts describe parallel lines. The answer is 0.

Classifying a System

Objective: Explain and use classifying a system in an Algebra 1 problem.

A two-line system has one, zero, or infinitely many solutions according to whether the lines intersect, are distinct parallel, or coincide. Equal slopes can describe parallel or identical lines.

Worked examples

Try itExample 3.1: How many intersections do y=3x+37 and y=3x+38 have?Show answer

0. Equal slopes with different intercepts describe parallel lines. The answer is 0.

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