Linear · Forms of a line · 1.2

Slope & y-intercept.

Given any line in y = mx + b, you can read both the slope and the y-intercept directly. y = −3x + 5 falls 3 for each step right and crosses the y-axis at 5.

01 / THE IDEA

See it work.

Watch the method

Slope & y-intercept

y = −3x + 5 → slope −3, intercept 5.

1 / 1
y=−3x+5y = -3x + 5
-8-888b
1

Read m and b

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

m=−3,  b=5m = -3,\; b = 5
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.

Both at once

The form hands you the slope and the intercept with no work.

Why it works

Negative slope falls left-to-right.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

What is the slope of y=x+6?

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = 1,\; b = 6

EX 2medium

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

1

Read m and b

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

EX 3hard

What is the slope of y=2x+1?

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = 2,\; b = 1

04 / COMMON TRAPS

Where students slip.

Trap

Sign errors on m.

Fix

A minus in front means a negative slope.

Trap

Confusing the two.

Fix

m is steepness; b is where it starts.

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=3x+6?

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
C2

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
C3

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
C4

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
Apply

Apply (4)

A1

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
A2

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
A3

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
A4

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
Extension

Extension (4)

E1

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
E2

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
E3

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.
E4

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

Need a hint?
  • m is the x-coefficient.
  • b is the constant.