Graphs · y = mx + b · 5.5

Find a point on the line.

Any point on the line satisfies its equation. To find the y for a given x (or vice versa), substitute into y = mx + b and solve. For y = 2x − 1 at x = 4, y = 7 → (4, 7) is on the line.

01 / THE IDEA

See it work.

Watch the method

Find a point on the line

y = 2x − 1, x = 4 → y = 7 → (4, 7).

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1

Substitute x

Put x = 4 into the equation.

y=2x−1,  x=4y = 2x - 1,\; x = 4
2

Compute y

Evaluate to find y.

y=7y = 7
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.

On the line

A point is on the line exactly when its coordinates fit the equation; substitute the known coordinate and solve.

Why it works

x = 4 → y = 7.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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 = 3

EX 2medium

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

1

Substitute x

Put x = -4 into the equation. y = 3x + 3, x = -4

2

Compute y

Evaluate to find y. y = -9

EX 3hard

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

1

Substitute x

Put x = -3 into the equation. y = -x - 4, x = -3

2

Compute y

Evaluate to find y. y = -1

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting to use the slope and intercept.

Fix

Substitute into the full y = mx + b.

Trap

Mixing up x and y.

Fix

Substitute the value you know for its variable.

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-3, find y when x = -4.

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
C2

For y=-1x+4, find y when x = 0.

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
C3

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

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
C4

For y=1x-5, find y when x = 3.

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
Apply

Apply (4)

A1

For y=1x+5, find y when x = 3.

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
A2

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

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
A3

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

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
A4

For y=2x+3, find y when x = 0.

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
Extension

Extension (4)

E1

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

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
E2

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

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
E3

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

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.
E4

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

Need a hint?
  • Substitute the known value.
  • Solve for the other coordinate.