Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines whether systems have a solution based upon their slope and y-intercepts.

Concepts

graphing systems of equations, systems of equations, systems of linear equations, solutions, solving systems by graphing, parallel lines, slope, y-intercepts

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Additional Tags

math

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Instructional Ideas

• Use technology to graph the lines using a large scale to cement the concept that lines with the same slope do not intersect
• Have individuals graph the equations in the problem set to verify their responses

Classroom Considerations

• Discussion of the proof about parallel lines addresses the high school standard HSG-GPE.B.5

Pros

• Includes alternative exercises to replace the proof
• For answers that have several answers that would be correct, the answer key provides a description of the correct response along with a sample answer

Cons

• None

Common Core

8.EE.C.8.a 8.EE.C.8.b MP3 MP8