Linear · Writing equations · 2.4

Parallel & perpendicular.

Parallel lines have EQUAL slopes. Perpendicular lines have slopes that are negative reciprocals (flip and change the sign): a line with slope 2 is perpendicular to one with slope −½.

01 / THE IDEA

See it work.

Watch the method

Parallel & perpendicular

Parallel: same slope. Perpendicular: negative reciprocal.

1 / 1
parallel to slope 2\text{parallel to slope } 2
-8-888
1

Same slope

Parallel lines have equal slopes.

m=2m = 2
— / WHY IT WORKS

The idea underneath.

Slope relationships

Same slope → parallel. Slopes multiplying to −1 (flip + negate) → perpendicular.

Why it works

2 and −½ are perpendicular.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A line has slope 3. What is the slope of a line parallel to it?

1

Answer

3

EX 2medium

A line has slope 3. What is the slope of a line parallel to it?

1

Answer

3

EX 3hard

A line has slope 3. What is the slope of a line parallel to it?

1

Answer

3

04 / COMMON TRAPS

Where students slip.

Trap

Only negating (not flipping).

Fix

Perpendicular slope flips AND negates.

Trap

Thinking perpendicular slopes are equal.

Fix

That’s parallel; perpendicular are negative reciprocals.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

A line has slope -2. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
C2

A line has slope -3. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
C3

A line has slope 3. What is the slope of a line perpendicular to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
C4

A line has slope -1. What is the slope of a line perpendicular to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
Apply

Apply (4)

A1

A line has slope 3. What is the slope of a line perpendicular to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
A2

A line has slope -2. What is the slope of a line perpendicular to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
A3

A line has slope -2. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
A4

A line has slope -3. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
Extension

Extension (4)

E1

A line has slope 3. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
E2

A line has slope 3. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
E3

A line has slope 3. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.
E4

A line has slope 3. What is the slope of a line parallel to it?

Need a hint?
  • Parallel → same slope.
  • Perpendicular → flip and negate.