Geometry
Perpendicular Line Through a Point Worksheets
Write perpendicular line equations through a given point, including exact fractional slopes and horizontal or vertical cases.
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Parallel Line Through a Point Worksheets
Write the equation of a distinct parallel line through a given point, using slope-intercept, standard or mixed input equations.
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Write each requested equation in slope-intercept form when possible; use x = c for a vertical line.
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Parallel lines have equal slopes. Use the supplied point to find the new intercept.
Learning objective
What this activity builds
Use equal slopes and a given point to write a parallel line equation.
Worked example
Find the line parallel to y = 2x + 1 through (3, 4).
y = 2x - 2.
Parallel lines have slope 2. Substitute the point: 4 = 2(3) + b, so b = -2.
Teaching notes
Make the practice count
- Keep the slope and solve for the new intercept.
- For a vertical source line, the parallel line is x equal to the new point’s x-coordinate.
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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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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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