Linear · Forms of a line · 1.3

x- and y-intercepts.

The y-intercept is where the line crosses the y-axis (x = 0): that’s b. The x-intercept is where it crosses the x-axis (y = 0): set y = 0 and solve. For y = 2x − 4, the x-intercept is 2.

01 / THE IDEA

See it work.

Watch the method

x- and y-intercepts

y = 2x − 4 → x-intercept 2, y-intercept −4.

1 / 2
y=2x−4y = 2x - 4
-8-888b
1

y-intercept (x = 0)

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

y-int=−4y\text{-int} = -4
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 the axes

Each intercept is found by setting the other variable to zero.

Why it works

On the y-axis, x = 0; on the x-axis, y = 0.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

1

y-intercept (x = 0)

Set x = 0; the constant b is the y-intercept. y-int = -2

2

x-intercept (y = 0)

Set y = 0 and solve: x = −b ÷ m. x-int = 2/3

EX 2medium

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

1

y-intercept (x = 0)

Set x = 0; the constant b is the y-intercept. y-int = 2

2

x-intercept (y = 0)

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

EX 3hard

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

1

y-intercept (x = 0)

Set x = 0; the constant b is the y-intercept. y-int = -4

2

x-intercept (y = 0)

Set y = 0 and solve: x = −b ÷ m. x-int = -4

04 / COMMON TRAPS

Where students slip.

Trap

Swapping the intercepts.

Fix

x-int is on the x-axis (y = 0).

Trap

Forgetting to solve for the x-intercept.

Fix

Set y = 0 and solve for x.

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=2x-5.

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
C2

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
C3

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
C4

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
Apply

Apply (4)

A1

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
A2

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
A3

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
A4

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
Extension

Extension (4)

E1

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
E2

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
E3

Find the x-intercept of y=2x-4.

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.
E4

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

Need a hint?
  • x-intercept: set y = 0.
  • Solve for x.