Graphs · y = mx + b · 5.1

The y-intercept.

In y = mx + b, the number b is the y-intercept — the y-value where the line crosses the y-axis (where x = 0). For y = 2x − 3, the y-intercept is −3, the point (0, −3).

01 / THE IDEA

See it work.

Watch the method

The y-intercept

y = 2x − 3 crosses the y-axis at −3.

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1

Read the y-intercept

In y = mx + b, the y-intercept is b — where the line crosses the y-axis.

y=2x−3⇒b=−3y = 2x - 3 \Rightarrow b = -3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 5.

streak 0
best 0
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Your answer:
— / WHY IT WORKS

The idea underneath.

b = the start

The y-intercept is the line’s value when x = 0 — the constant b in y = mx + b.

Why it works

(0, b) is on the y-axis.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

What is the y-intercept of y=3x+1?

1

Read the y-intercept

In y = mx + b, the y-intercept is b — where the line crosses the y-axis. y = 3x + 1 ⇒ b = 1

EX 2medium

What is the y-intercept of y=-2x-1?

1

Read the y-intercept

In y = mx + b, the y-intercept is b — where the line crosses the y-axis. y = -2x - 1 ⇒ b = -1

EX 3hard

What is the y-intercept of y=-3x+6?

1

Read the y-intercept

In y = mx + b, the y-intercept is b — where the line crosses the y-axis. y = -3x + 6 ⇒ b = 6

04 / COMMON TRAPS

Where students slip.

Trap

Reading the slope as the intercept.

Fix

b is the constant, not the x-coefficient.

Trap

Forgetting it’s a y-value.

Fix

The intercept is at (0, b).

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 y-intercept of y=-1x-5?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
C2

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

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
C3

What is the y-intercept of y=2x+6?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
C4

What is the y-intercept of y=3x-3?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
Apply

Apply (4)

A1

What is the y-intercept of y=-1x-2?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
A2

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

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
A3

What is the y-intercept of y=2x+6?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
A4

What is the y-intercept of y=-1x-5?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
Extension

Extension (4)

E1

What is the y-intercept of y=1x+6?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
E2

What is the y-intercept of y=-3x+6?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
E3

What is the y-intercept of y=-2x-1?

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.
E4

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

Need a hint?
  • Find b in y = mx + b.
  • It’s the y-value at x = 0.