Linear · Writing equations · 2.2

From slope & a point.

Given a slope and a point, substitute the point into y = mx + b to find b, then write the equation. Slope 3 through (2, 1): 1 = 3(2) + b → b = −5 → y = 3x − 5.

01 / THE IDEA

See it work.

Watch the method

From slope & a point

m = 3 through (2, 1) → y = 3x − 5.

1 / 2
m=3,  (2,1)m = 3,\; (2,1)
-8-888
1

Use the point and slope

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

1=3(2)+b1 = 3(2) + b
2

Write the equation

Put m and b together.

y=3x−5y = 3x - 5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type y = mx + b.

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

The idea underneath.

Solve for b

Plug the point’s coordinates into y = mx + b and solve for the missing intercept.

Why it works

1 = 6 + b → b = −5.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write the equation of the line with slope -3 through (4,-5).

1

Use the point and slope

Substitute the point into y = mx + b and solve for b. -5 = -3(4) + b

2

Write the equation

Put m and b together. y = -3x + 7

EX 2medium

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

1

Use the point and slope

Substitute the point into y = mx + b and solve for b. -4 = -1(-3) + b

2

Write the equation

Put m and b together. y = -x - 7

EX 3hard

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

1

Use the point and slope

Substitute the point into y = mx + b and solve for b. 4 = -2(4) + b

2

Write the equation

Put m and b together. y = -2x + 12

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting to solve for b.

Fix

Use the point to find the intercept.

Trap

Swapping x and y from the point.

Fix

x goes with the slope; y is the output.

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 with slope 2 through (4,1).

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
C2

Write the equation of the line with slope 3 through (-4,-5).

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
C3

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

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
C4

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

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
Apply

Apply (4)

A1

Write the equation of the line with slope 1 through (3,2).

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
A2

Write the equation of the line with slope 1 through (2,4).

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
A3

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

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
A4

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

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
Extension

Extension (4)

E1

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

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
E2

Write the equation of the line with slope 2 through (4,6).

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
E3

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

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.
E4

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

Need a hint?
  • Substitute the point into y = mx + b.
  • Solve for b.