Graphs · Graphing relationships · 3.1

Plot from a table.

A table of x and y values is a list of points (x, y). Plug an x into the rule to get y, then plot the pair. For y = 2x + 1 at x = 3, y = 7 → plot (3, 7).

01 / THE IDEA

See it work.

Watch the method

Plot from a table

y = 2x + 1, x = 3 → y = 7 → point (3, 7).

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1

Substitute x

Put x = 3 into the equation.

y=2x+1,  x=3y = 2x + 1,\; x = 3
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.

streak 0
best 0
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Your answer:
— / WHY IT WORKS

The idea underneath.

Rows to points

Evaluate the rule for each x to get y; each pair is a point on the graph.

Why it works

x = 3 → y = 7 → (3, 7).

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

1

Substitute x

Put x = -2 into the equation. y = 2x + 3, x = -2

2

Compute y

Evaluate to find y. y = -1

EX 2medium

For y=3x-4, find y when x = 2.

1

Substitute x

Put x = 2 into the equation. y = 3x - 4, x = 2

2

Compute y

Evaluate to find y. y = 2

EX 3hard

For y=1x+2, find y when x = 4.

1

Substitute x

Put x = 4 into the equation. y = x + 2, x = 4

2

Compute y

Evaluate to find y. y = 6

04 / COMMON TRAPS

Where students slip.

Trap

Plotting (y, x).

Fix

Keep the order (x, y).

Trap

Mis-evaluating the rule.

Fix

Substitute x carefully.

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

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
C2

For y=-2x+3, find y when x = 4.

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
C3

For y=1x+2, find y when x = 0.

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
C4

For y=-3x-5, find y when x = -2.

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
Apply

Apply (4)

A1

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

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
A2

For y=-1x+2, find y when x = -3.

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
A3

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

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
A4

For y=-1x+5, find y when x = 2.

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
Extension

Extension (4)

E1

For y=2x-4, find y when x = 1.

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
E2

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

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
E3

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

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).
E4

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

Need a hint?
  • Substitute x into the rule for y.
  • Plot the pair (x, y).