NY Next Generation Math GEO-G.GPE.5.b

MathGrades 9–12On the coordinate plane:

The Standard

Determine if lines are parallel, perpendicular, or neither, based on their slopes

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students calculate slopes to classify two lines as parallel, perpendicular, or neither. They account for equal slopes, negative reciprocals, and vertical-horizontal pairs.
What Mastery Looks Like: The student finds both slopes accurately and states the matching relationship. Equations, tables, or coordinate pairs are handled consistently, including undefined slopes.
Common Misconceptions: Students may compare intercepts instead of slopes or label opposite slopes perpendicular. They may mishandle vertical lines or simplify a negative reciprocal incorrectly.
How to Assess It: Give three line pairs in mixed forms. Ask students to classify each pair and show the slope evidence.

Lesson moves

Plot line pairs from coordinate cards and verify their visual relationship with calculated slopes.
Ask why different intercepts do not prevent two lines from being parallel.
Play parallel-perpendicular-neither relay with equations, point pairs, and slope cards.
Check whether proposed road or wall segments meet a parallel or perpendicular design requirement.

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