Where it cuts the y-axis

The idea

Any line y = ax + b cuts the y-axis at (0, b); b is its y-intercept, with a positive b above the origin and a negative b below it.

Cutting the y-axis

The line y = 2x + 5 meets the y-axis at the point where x = 0. Put x = 0 into 2x + 5 and see what y is. The lines y = x + 3 and y = 3x − 2 meet the y-axis too.

Where do you think y = 2x + 5 cuts the y-axis?

• At (0, 5)
• At (0, 2)
• At (5, 0)

Move the line up and down

Change b and watch the orange point where the line cuts the y-axis.

The y-intercept b

Any line y = ax + b cuts the y-axis at (0, b). The number b is the y-intercept: above the origin if b is positive, below the origin if b is negative.

y = 2x + 5 cuts the y-axis at (0, 5). y = x + 3 cuts it at (0, 3). y = 3x − 2 cuts it at (0, −2).

Notes

y = ax + b cuts the y-axis at (0, b). The y-intercept is b.

Check yourself

Where does y = x + 3 cut the y-axis? Give the y-coordinate.

Answer: 3

When x = 0, y = 0 + 3 = 3. The line cuts the y-axis at (0, 3).

What is the y-intercept of the line y = 3x − 2?

Answer: -2

In y = 3x + (−2), b = −2. The line cuts the y-axis at (0, −2), below the origin.

A line cuts the y-axis at (0, −4). Which could be its equation?

The y-intercept of a line is positive. Where does it cut the y-axis?

• y = 2x − 4 — correct. Yes. b = −4.
• y = 2x + 4. That line cuts the y-axis at (0, 4).
• y = −4x. That line passes through the origin.
• Below the origin. Below the origin is for negative b.
• Above the origin — correct. Yes. Positive b means above the origin.
• At the origin. At the origin is for b = 0.