Graphs · y = mx + b · 5.2

What y = mx + b means.

In y = mx + b, m is the slope (steepness) and b is the y-intercept (start). The equation gives the y for any x. For y = 3x − 2 at x = 2, y = 4.

01 / THE IDEA

See it work.

Watch the method

What y = mx + b means

m is the slope, b is the start; plug in x for y.

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1

Substitute x

Put x = 2 into the equation.

y=3x−2,  x=2y = 3x - 2,\; x = 2
2

Compute y

Evaluate to find y.

y=4y = 4
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 5.

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Your answer:
— / WHY IT WORKS

The idea underneath.

Two numbers, one line

m sets the steepness and direction; b sets where it crosses the y-axis. Together they fix the line.

Why it works

Start at b, climb by m.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

For y=-1x+3, find y when x = -3.

1

Substitute x

Put x = -3 into the equation. y = -x + 3, x = -3

2

Compute y

Evaluate to find y. y = 6

EX 2medium

For y=-2x-1, find y when x = 2.

1

Substitute x

Put x = 2 into the equation. y = -2x - 1, x = 2

2

Compute y

Evaluate to find y. y = -5

EX 3hard

For y=-2x-2, find y when x = 4.

1

Substitute x

Put x = 4 into the equation. y = -2x - 2, x = 4

2

Compute y

Evaluate to find y. y = -10

04 / COMMON TRAPS

Where students slip.

Trap

Swapping m and b.

Fix

m multiplies x (slope); b is the constant (intercept).

Trap

Forgetting the sign of b.

Fix

A minus makes the intercept negative.

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

For y=3x+5, find y when x = 0.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
C2

For y=2x+5, find y when x = -1.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
C3

For y=1x-5, find y when x = -2.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
C4

For y=1x-4, find y when x = 3.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
Apply

Apply (4)

A1

For y=2x+1, find y when x = 3.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
A2

For y=-1x+5, find y when x = 2.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
A3

For y=-3x-3, find y when x = 1.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
A4

For y=1x-1, find y when x = 3.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
Extension

Extension (4)

E1

For y=-2x+3, find y when x = 2.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
E2

For y=1x+4, find y when x = 1.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
E3

For y=3x+4, find y when x = 2.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.
E4

For y=2x-2, find y when x = -1.

Need a hint?
  • m is the slope; b is the intercept.
  • Substitute x to find y.