2-7: Perpendicular Lines

By Oscar Castanos

​ 📅 Integrated Math I • Objective 2-7 Objective:
🎯 I can write and graph parallel and perpendicular lines.
Sub-Objective: 🧩 I can determine the slope of a line perpendicular to a given line and write its equation through a specific point.
Warm-Up:
1️⃣ Review – Write an equation of a line parallel to y = 2x + 3 that passes through (1, 4).
2️⃣ Lead-In – If a line has slope 2, what would be the slope of a line perpendicular to it?

Today’s Plan:
Warm-Up & Review
Notes: Slopes of Perpendicular Lines
Mild → Medium Practice
Think-Pair-Share & Error Analysis
Check Your Understanding (CYU)

Expectations: Phones in slots 📱 | Notebooks open ✏️ | Work in pairs 🧠 | Respect voices 💬 |

​Warm-Up:
1️⃣ Review – Write an equation of a line parallel to y = 2x + 3 that passes through (1, 4).



2️⃣ Lead-In – If a line has slope 2, what would be the slope of a line perpendicular to it?

​Mild:
Example 1: Find a Perpendicular Slope Given y = 3x + 1. What is the slope of a line perpendicular to it?

​Mild (Student Try)
Find the slope of a line perpendicular to each:
a. y = –2x + 5
b. y = ½x – 1
c. y = –¾x + 7
Think-Pair-Share #1:
Partner A – state the rule for perpendicular slopes.
Partner B – check each answer.

​Medium:


Example 2 – Write the equation of the line perpendicular to y = 2x + 1 that passes through (3, –2).

Open Ended

Write an equation of a line perpendicular to y = –3x + 2 that passes through (0, 4).

Open Ended

Write an equation of a line perpendicular to y = ½x – 1 that passes through (2, –3).

​Error Analysis:
A student says “The line perpendicular to y = 3x + 2 that passes (-3,6) is y = ⅓x – 1.”


Answer:
1. What rule did the student miss?

2. What should the correct slope be?

3. How can we verify two lines are perpendicular?

​CYU (Check Your Understanding):

Mild:
1. Find the slope of a line perpendicular to y = –5x + 1.

Medium:
2. Write the equation of a line perpendicular to y = 3x + 2, through (4, 1).
3. Write the equation of a line perpendicular to 3x + 2y = 6, through (6, 3).

Spicy (Application):
3. A road runs along two street corners whose coordinates on the city map are (3, 5) and (9, 9). Design a driveway that meets it at a right angle and passes through (2, 3). Write its equation and sketch both lines.