Graphs · Slope · 4.3

Types of slope.

A line’s slope can be positive (uphill left-to-right), negative (downhill), zero (horizontal), or undefined (vertical, since you can’t divide by a zero run).

01 / THE IDEA

See it work.

Watch the method

Types of slope

Uphill +, downhill −, flat 0, vertical undefined.

1 / 1
-6-666
1

Which way does it lean?

Uphill → positive, downhill → negative, flat → zero, vertical → undefined.

negative\text{negative}
— / WHY IT WORKS

The idea underneath.

Four kinds

Up → positive, down → negative, flat (no rise) → zero, vertical (no run) → undefined.

Why it works

A flat line has slope 0; a vertical line is undefined.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

The line through (1,3) and (2,-1) has what kind of slope?

1

Answer

Negative

EX 2medium

The line through (1,-6) and (6,-5) has what kind of slope?

1

Answer

Positive

EX 3hard

The line through (2,-2) and (1,6) has what kind of slope?

1

Answer

Negative

04 / COMMON TRAPS

Where students slip.

Trap

Calling a horizontal line undefined.

Fix

Horizontal is slope 0; vertical is undefined.

Trap

Mixing up + and −.

Fix

Read left to right: up is +, down is −.

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

The line through (-2,2) and (-4,-5) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
C2

The line through (6,6) and (-2,2) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
C3

The line through (-4,2) and (-2,-6) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
C4

The line through (4,-3) and (2,6) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
Apply

Apply (4)

A1

The line through (6,-6) and (4,-4) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
A2

The line through (5,1) and (-1,6) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
A3

The line through (6,2) and (6,2) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
A4

The line through (6,-5) and (-1,-4) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
Extension

Extension (4)

E1

The line through (6,6) and (2,3) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
E2

The line through (4,6) and (-2,-1) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
E3

The line through (-4,-4) and (5,6) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.
E4

The line through (5,6) and (1,-3) has what kind of slope?

Need a hint?
  • Which way does it lean?
  • Flat → 0; vertical → undefined.