Linear · Graphing lines · 3.3

Horizontal & vertical.

A horizontal line y = c has slope 0 (no rise). A vertical line x = c has an undefined slope (no run — you can’t divide by zero). y = 4 is flat; x = 3 is straight up.

01 / THE IDEA

See it work.

Watch the method

Horizontal & vertical

y = 4 → slope 0; x = 3 → slope undefined.

1 / 1
y=4y = 4
-8-888b
1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept.

m=0,  b=4m = 0,\; b = 4
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number.

streak 0
best 0
-8-888
…
Answer:
— / WHY IT WORKS

The idea underneath.

Flat vs straight up

No rise → slope 0; no run → undefined slope.

Why it works

y = c stays level; x = c stands up.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

What is the slope of y=-3x-1?

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = -3,\; b = -1

EX 2medium

What is the slope of y=-3x+4?

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = -3,\; b = 4

EX 3hard

What is the slope of y=-2x-5?

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = -2,\; b = -5

04 / COMMON TRAPS

Where students slip.

Trap

Calling a horizontal line undefined.

Fix

Horizontal is slope 0; vertical is undefined.

Trap

Writing y = c as a slope.

Fix

Its slope is 0, and its equation is y = c.

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

What is the slope of y=x-5?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
C2

What is the slope of y=x-2?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
C3

What is the slope of y=2x-3?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
C4

What is the slope of y=-x+4?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
Apply

Apply (4)

A1

What is the slope of y=3x-1?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
A2

What is the slope of y=-3x-6?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
A3

What is the slope of y=-x+4?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
A4

What is the slope of y=-x+4?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
Extension

Extension (4)

E1

What is the slope of y=3x-2?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
E2

What is the slope of y=3x+3?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
E3

What is the slope of y=3x-5?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.
E4

What is the slope of y=-x+4?

Need a hint?
  • Horizontal → slope 0.
  • Vertical → undefined.