Linear · Writing equations · 2.3

From two points.

From two points: first find the slope (rise ÷ run), then use one point to find b. Through (0, 2) and (1, 5): slope 3, and b = 2 → y = 3x + 2.

01 / THE IDEA

See it work.

Watch the method

From two points

(0,2),(1,5) → slope 3, b 2 → y = 3x + 2.

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(0,2), (1,5)(0,2),\, (1,5)
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1

Find the slope

Slope = rise ÷ run between the points.

m=3m = 3
2

Find b, then write it

Use a point to find b, then write y = mx + b.

y=3x+2y = 3x + 2
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.

Two-step build

Compute the slope between the points, then plug one point in to get b.

Why it works

Slope first, intercept second.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write the equation of the line through (-2,0) and (0,-4).

1

Find the slope

Slope = rise ÷ run between the points. m = -2

2

Find b, then write it

Use a point to find b, then write y = mx + b. y = -2x - 4

EX 2medium

Write the equation of the line through (-3,-10) and (-1,-4).

1

Find the slope

Slope = rise ÷ run between the points. m = 3

2

Find b, then write it

Use a point to find b, then write y = mx + b. y = 3x - 1

EX 3hard

Write the equation of the line through (-3,4) and (0,1).

1

Find the slope

Slope = rise ÷ run between the points. m = -1

2

Find b, then write it

Use a point to find b, then write y = mx + b. y = -x + 1

04 / COMMON TRAPS

Where students slip.

Trap

Mixing the slope formula order.

Fix

Subtract y’s and x’s in the same order.

Trap

Skipping the b step.

Fix

You still need the intercept.

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 the equation of the line through (-1,-7) and (0,-4).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
C2

Write the equation of the line through (-2,-6) and (0,-4).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
C3

Write the equation of the line through (1,6) and (4,15).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
C4

Write the equation of the line through (1,7) and (3,13).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
Apply

Apply (4)

A1

Write the equation of the line through (-1,6) and (0,4).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
A2

Write the equation of the line through (-1,-2) and (1,4).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
A3

Write the equation of the line through (0,3) and (3,-3).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
A4

Write the equation of the line through (-1,2) and (0,1).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
Extension

Extension (4)

E1

Write the equation of the line through (-2,-10) and (0,-4).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
E2

Write the equation of the line through (1,2) and (4,5).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
E3

Write the equation of the line through (1,5) and (3,11).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.
E4

Write the equation of the line through (-2,1) and (-1,2).

Need a hint?
  • Find the slope between the points.
  • Use a point to find b.