Linear · Writing equations · 2.1

From slope & intercept.

If you know the slope and the y-intercept, just substitute them into y = mx + b. Slope 2 and intercept 3 give y = 2x + 3.

01 / THE IDEA

See it work.

Watch the method

From slope & intercept

m = 2, b = 3 → y = 2x + 3.

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m=2,  (0,3)m = 2,\; (0,3)
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1

Use the point and slope

Substitute the point into y = mx + b and solve for b.

3=2(0)+b3 = 2(0) + b
2

Write the equation

Put m and b together.

y=2x+3y = 2x + 3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type y = mx + b.

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Answer:
— / WHY IT WORKS

The idea underneath.

Substitute

The slope goes in front of x; the intercept is the constant.

Why it works

Just fill in the form.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write the equation of the line with slope 1 through (4,-1).

1

Use the point and slope

Substitute the point into y = mx + b and solve for b. -1 = 1(4) + b

2

Write the equation

Put m and b together. y = x - 5

EX 2medium

Write the equation of the line with slope -3 through (3,-4).

1

Use the point and slope

Substitute the point into y = mx + b and solve for b. -4 = -3(3) + b

2

Write the equation

Put m and b together. y = -3x + 5

EX 3hard

Write the equation of the line with slope 3 through (2,6).

1

Use the point and slope

Substitute the point into y = mx + b and solve for b. 6 = 3(2) + b

2

Write the equation

Put m and b together. y = 3x

04 / COMMON TRAPS

Where students slip.

Trap

Swapping m and b.

Fix

m multiplies x; b is the constant.

Trap

Dropping a sign.

Fix

Keep signs on both.

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.

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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 the equation of the line with slope -3 through (1,-6).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
C2

Write the equation of the line with slope -3 through (-3,-3).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
C3

Write the equation of the line with slope -2 through (2,4).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
C4

Write the equation of the line with slope 3 through (-2,4).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
Apply

Apply (4)

A1

Write the equation of the line with slope -2 through (-1,6).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
A2

Write the equation of the line with slope 3 through (-2,5).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
A3

Write the equation of the line with slope -3 through (2,2).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
A4

Write the equation of the line with slope -1 through (-4,5).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
Extension

Extension (4)

E1

Write the equation of the line with slope 3 through (-4,-6).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
E2

Write the equation of the line with slope 3 through (-4,1).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
E3

Write the equation of the line with slope -2 through (-4,5).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.
E4

Write the equation of the line with slope -2 through (-2,-2).

Need a hint?
  • Put the slope in front of x.
  • Add the intercept.