Linear · Graphing lines · 3.2

Graph from intercepts.

A line can be graphed from its two intercepts: plot where it crosses each axis, then connect. Find the x-intercept (set y = 0) and the y-intercept (set x = 0), then draw.

01 / THE IDEA

See it work.

Watch the method

Graph from intercepts

Plot the x- and y-intercepts, then connect.

1 / 2
y=3x−6y = 3x - 6
-8-888b
1

y-intercept (x = 0)

Set x = 0; the constant b is the y-intercept.

y-int=−6y\text{-int} = -6
2

x-intercept (y = 0)

Set y = 0 and solve: x = −b ÷ m.

x-int=2x\text{-int} = 2
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number.

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

The idea underneath.

Cross both axes

The two intercepts are two points on the line — enough to draw it.

Why it works

Connect the axis crossings.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the x-intercept of y=-3x-3.

1

y-intercept (x = 0)

Set x = 0; the constant b is the y-intercept. y-int = -3

2

x-intercept (y = 0)

Set y = 0 and solve: x = −b ÷ m. x-int = -1

EX 2medium

Find the x-intercept of y=-3x-6.

1

y-intercept (x = 0)

Set x = 0; the constant b is the y-intercept. y-int = -6

2

x-intercept (y = 0)

Set y = 0 and solve: x = −b ÷ m. x-int = -2

EX 3hard

Find the x-intercept of y=x+6.

1

y-intercept (x = 0)

Set x = 0; the constant b is the y-intercept. y-int = 6

2

x-intercept (y = 0)

Set y = 0 and solve: x = −b ÷ m. x-int = -6

04 / COMMON TRAPS

Where students slip.

Trap

Plotting only one intercept.

Fix

You need two points.

Trap

Mislabeling which axis.

Fix

x-int on the x-axis, y-int on the y-axis.

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

Find the x-intercept of y=x-4.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
C2

Find the x-intercept of y=-3x+4.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
C3

Find the x-intercept of y=-x-5.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
C4

Find the x-intercept of y=-x+5.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
Apply

Apply (4)

A1

Find the x-intercept of y=-2x-5.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
A2

Find the x-intercept of y=-3x+3.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
A3

Find the x-intercept of y=3x-4.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
A4

Find the x-intercept of y=x-3.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
Extension

Extension (4)

E1

Find the x-intercept of y=-2x+1.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
E2

Find the x-intercept of y=-3x-1.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
E3

Find the x-intercept of y=3x-5.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.
E4

Find the x-intercept of y=-2x-3.

Need a hint?
  • Find both intercepts.
  • Plot and connect them.