Linear · Forms of a line · 1.4

Standard → slope-intercept.

Standard form Ax + By = C can be rewritten as y = mx + b by solving for y: move the x term over and divide by the y-coefficient. 2x + 3y = 6 → 3y = −2x + 6 → y = −⅔x + 2.

01 / THE IDEA

See it work.

Watch the method

Standard → slope-intercept

2x + 3y = 6 → y = −⅔x + 2.

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2x+3y=62x + 3y = 6
-8-888b
1

Solve for y

Move the x term to the right, then divide by the y-coefficient.

2x+3y=62x+3y=6
2

Slope-intercept form

Now it is y = mx + b.

y=−23x+2y = -\frac{2}{3}x + 2
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type y = mx + b.

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

The idea underneath.

Isolate y

Subtract the x term from both sides, then divide every term by the y-coefficient.

Why it works

3y = −2x + 6 → divide by 3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write 3x+3y=8 in slope-intercept form (y = mx + b).

1

Solve for y

Move the x term to the right, then divide by the y-coefficient. 3x+3y=8

2

Slope-intercept form

Now it is y = mx + b. y = -x + 8/3

EX 2medium

Write 3x+4y=-5 in slope-intercept form (y = mx + b).

1

Solve for y

Move the x term to the right, then divide by the y-coefficient. 3x+4y=-5

2

Slope-intercept form

Now it is y = mx + b. y = -3/4x - 5/4

EX 3hard

Write 4x+2y=1 in slope-intercept form (y = mx + b).

1

Solve for y

Move the x term to the right, then divide by the y-coefficient. 4x+2y=1

2

Slope-intercept form

Now it is y = mx + b. y = -2x + 1/2

04 / COMMON TRAPS

Where students slip.

Trap

Dividing only one term.

Fix

Divide the WHOLE side by the y-coefficient.

Trap

Sign error moving the x term.

Fix

Subtract it from both sides.

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

Write 4x+4y=-2 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
C2

Write 4x+2y=3 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
C3

Write 4x+3y=-5 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
C4

Write 1x+3y=-6 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
Apply

Apply (4)

A1

Write 1x+2y=6 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
A2

Write 3x+2y=-7 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
A3

Write 2x+1y=-7 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
A4

Write 2x+1y=-3 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
Extension

Extension (4)

E1

Write 4x+4y=-8 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
E2

Write 2x+2y=3 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
E3

Write 3x+1y=8 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.
E4

Write 3x+4y=8 in slope-intercept form (y = mx + b).

Need a hint?
  • Move the x term to the right.
  • Divide every term by the y-coefficient.