Parallel and Perpendicular Lines | Find the Slope and Write the Equation

📚 Learn How to Identify and Write Equations for Parallel and Perpendicular Lines! In this video, you'll learn how to:
✔ Understand how slopes determine the relationship between lines
✔ Write the equation of a line parallel to a given line
✔ Write the equation of a line perpendicular to a given line
✔ Determine if two lines are parallel, perpendicular, or neither

We walk through step-by-step examples using point-slope form and discuss how to recognize slope relationships from equations written in standard form or slope-intercept form.

🔍 What You’ll Learn in This Video:
✅ Slopes of Parallel and Perpendicular Lines:
✔ Parallel lines have the same slope
✔ Perpendicular lines have opposite reciprocal slopes (e.g., m = 2 → perpendicular slope = -½)

✅ How to Write the Equation of a Line Given a Point and a Line:
✔ Use point-slope form: y - y₁ = m(x - x₁)
✔ For parallel lines: use the same slope as the given line
✔ For perpendicular lines: use the negative reciprocal of the slope

📊 Examples Covered in This Video:
✔ Find an equation of a line through (1, 2) parallel to 2x - y = 3
✔ Find an equation of a line through (1, −6) parallel to x + 2y = 6
✔ Find an equation of a line through (1, 2) perpendicular to 2x - y = 3
✔ Find an equation of a line through (-2, 2) perpendicular to 3x + y =4
✔ Determine if two lines are parallel, perpendicular, or neither:
 • y = 2x + 3 and 2y − 4x = 5
 • −3x + 4y = 4 and 4x + 3y = 5
 • 7x − 3y = 2 and 21x + 9y = 1

By the end of this video, you’ll be able to:
✔ Recognize slope relationships between two lines
✔ Write equations of parallel and perpendicular lines
✔ Use slope and point-slope form to model linear relationships

📥 Download Free Guided Notes!
Follow along and complete each example as you watch:
👉 https://www.understandthemath.com/algebra

*Prerequisite Algebra and Geometry Concepts*
https://youtu.be/Tgzp8TOHFW4
https://youtu.be/LyMESqKEVnY
https://youtu.be/YV0wFncCTGw
https://youtu.be/P_B6YBGKwVU
https://youtu.be/QlWekLztefU
https://youtu.be/22w_mqWly3w
https://youtu.be/pOu0JgbHazI
https://youtu.be/HHNcCzywscM
*Functions*
https://youtu.be/jcZvmA3rh1E
https://youtu.be/aPJZfzY9WGc
https://youtu.be/F0Dg-6LK9RA
https://youtu.be/Sqi57_oAAbc
https://youtu.be/Hm_RljsqCsM
https://youtu.be/ZYQGGx6ipqI
https://youtu.be/qYjgLsSXke8
https://youtu.be/qWAxHj_2PoM
https://youtu.be/bm0iesAFNLY
https://youtu.be/_gYnVDOctfc
https://youtu.be/sTDooyt29to
https://youtu.be/JhIibCdSNtU
https://youtu.be/DGmUHMut4eY
https://youtu.be/l3EvEcnxOEg
https://youtu.be/DfpTz2oXYpo
https://youtu.be/0ufcDZ1KISQ
https://youtu.be/ghEwqNCO9S8
https://youtu.be/PPxnBlqsvVs
https://youtu.be/gEORARhLf9s
https://youtu.be/0Z6QOt-NFww
https://youtu.be/0AeWF1ffwN8
https://youtu.be/W_wpVUaTcn0
*Linear Functions*
https://youtu.be/_mzxOXBAvUY
https://youtu.be/J16xpq5okLE
https://youtu.be/Ml_uNFH4SbE
https://youtu.be/dFT-2xdJHrM
https://youtu.be/UGaKAG1ZkUY
https://youtu.be/ItLsdupywFc
https://youtu.be/IgZ-5oqDlkQ
https://youtu.be/WmSoEkns6bc
https://youtu.be/JWkD9LgRXkg
https://youtu.be/2j2evehvVFU
https://youtu.be/Loi7UWJc9PY

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*Timestamps*
00:00 Introduction
00:33 Slope of Parallel and Perpendicular Lines
01:37 Examples - Equation of a Line Parallel to a Given Line
07:24 Examples - Equation of a Line Perpendicular to a Given Line
13:37 Examples - Determine if Two Lines are Parallel, Perpendicular, or Neither

*More About Understand The Math*
Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.

Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective.

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Видео Parallel and Perpendicular Lines | Find the Slope and Write the Equation канала Understand The Math