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Classify Lines from Equations Worksheets

Compare two linear equations and identify parallel, perpendicular or intersecting but not perpendicular lines, with worked slope reasoning.

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Classify each pair of distinct lines as parallel, perpendicular, or intersecting but not perpendicular.

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Paper sizes and printing help · More geometry activities

Compare exact slopes

Equal slopes identify distinct parallel lines. Negative reciprocals identify perpendicular lines; every other pair is intersecting but not perpendicular.

Learning objective

What this activity builds

Identify line relationships from equations in different forms.

Worked example

Classify y = 2x + 1 and y = -1/2 x + 3.

Perpendicular.

Their slopes multiply to -1, so the lines meet at a right angle.

Teaching notes

Make the practice count

  • For ax + by = c with b nonzero, the slope is -a/b.
  • Check vertical and horizontal lines by direction.

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Eight equation tasks use exact integer or fractional slopes. Choose slope-intercept, standard, or mixed input forms.

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Math SheetNameScoreTeacherDateClassify Lines from EquationsClassify each pair of distinct lines as parallel, perpendicular, or intersecting but not perpendicular.1. Classify the two lines.1)y=111x2)y=111x-1Classification:2. Classify the two lines.1)y=-102)x=1Classification:3. Classify the two lines.1)y=87x-42)y=-32x-3Classification:4. Classify the two lines.1)y=37x-102)3x-7y=-21Classification:5. Classify the two lines.1)11x-3y=32)11x-12y=-12Classification:6. Classify the two lines.1)7x-3y=-302)y=-37x-2Classification:7. Classify the two lines.1)x=02)x=-5Classification:8. Classify the two lines.1)9x-11y=1322)y=-53x+11Classification:Compare exact slopes. Keep undefined slopes distinct from zero slopes.math-sheet.comPage 1 of 1

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Related activities

First page preview: Classify Lines from Slopes Worksheets

Geometry

Classify Lines from Slopes Worksheets

Decide whether distinct lines are parallel, perpendicular or neither from their slopes, including fractions, zero and undefined slopes.

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