Graphs · Graphing relationships · 3.2

A table becomes a line.

When a relationship is linear, its plotted points fall on a straight line. Find a few points from the rule, plot them, and draw the line through them. y = 2x − 1 at x = 2 gives (2, 3).

01 / THE IDEA

See it work.

Watch the method

A table becomes a line

Plot several points from the rule; they form a line.

1 / 2
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1

Substitute x

Put x = 2 into the equation.

y=2x−1,  x=2y = 2x - 1,\; x = 2
2

Compute y

Evaluate to find y.

y=3y = 3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 5.

streak 0
best 0
-6-666
Your answer:
— / WHY IT WORKS

The idea underneath.

Connect the dots

Two or three points are enough; a straight rule gives a straight line.

Why it works

All the points line up.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

1

Substitute x

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

2

Compute y

Evaluate to find y. y = -12

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 = 15

EX 3hard

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

1

Substitute x

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

2

Compute y

Evaluate to find y. y = 5

04 / COMMON TRAPS

Where students slip.

Trap

Connecting non-collinear points.

Fix

For a linear rule all points line up — recheck a slip.

Trap

Using only one point.

Fix

Use at least two to draw the line.

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
C2

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
C3

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
C4

For y=1x+5, find y when x = -4.

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
Apply

Apply (4)

A1

For y=3x+5, find y when x = -4.

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
A2

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
A3

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
A4

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
Extension

Extension (4)

E1

For y=2x-5, find y when x = 4.

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
E2

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
E3

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.
E4

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

Need a hint?
  • Find two or three points.
  • Draw the straight line through them.