Linear · Forms of a line · 1.1

Slope-intercept form.

A line in slope-intercept form is y = mx + b: m is the slope (steepness/direction) and b is the y-intercept (where it crosses the y-axis). y = 2x + 3 has slope 2 and intercept 3.

01 / THE IDEA

See it work.

Watch the method

Slope-intercept form

y = 2x + 3 → slope 2, intercept 3.

1 / 1
y=2x+3y = 2x + 3
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1

Read m and b

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

m=2,  b=3m = 2,\; b = 3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number.

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

The idea underneath.

m and b

The number in front of x is the slope; the constant is the y-intercept.

Why it works

Climb by m, start at b.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = 3,\; b = -2

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=3x-2?

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = 3,\; b = -2

04 / COMMON TRAPS

Where students slip.

Trap

Reading b as the slope.

Fix

b is the constant; m multiplies x.

Trap

Dropping a negative.

Fix

Keep the sign on m and 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 slope of y=2x+1?

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
C2

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

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
C3

What is the slope of y=2x-6?

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
C4

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

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
Apply

Apply (4)

A1

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

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
A2

What is the slope of y=2x+6?

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
A3

What is the slope of y=x-1?

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
A4

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

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
Extension

Extension (4)

E1

What is the slope of y=2x+6?

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
E2

What is the slope of y=x+6?

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
E3

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

Need a hint?
  • Find the coefficient of x.
  • That is the slope.
E4

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

Need a hint?
  • Find the coefficient of x.
  • That is the slope.