y-axis
The y-axis is the vertical line in the coordinate plane. It runs straight up and down, crossing the horizontal x-axis at the origin (0, 0).
The y-axis is the vertical reference line in a two-dimensional coordinate system. It is perpendicular to the x-axis and intersects it at the origin. Every point on the y-axis has an x-coordinate of 0, so its points take the form . The y-axis divides the coordinate plane into its left and right halves.
Example
Problem: Plot the point (0, 4) and explain its relationship to the y-axis.
Step 1: Start at the origin (0, 0), where the x-axis and y-axis cross.
Step 2: The x-coordinate is 0, so you don't move left or right at all. You stay on the y-axis.
Step 3: The y-coordinate is 4, so move 4 units up from the origin along the y-axis.
Step 4: Mark the point. Because the x-coordinate is 0, this point sits directly on the y-axis.
Answer: The point (0, 4) lies on the y-axis, 4 units above the origin. Any point with an x-coordinate of 0 is located on the y-axis.
Visualization
Why It Matters
The y-axis is one of the two building blocks of every coordinate grid you'll use in math and science. When you graph an equation like , the place where the line crosses the y-axis (the y-intercept) often tells you something meaningful — like a starting value before any change occurs. Scientists, economists, and engineers all rely on the y-axis to display data such as temperature, cost, or height.
Common Mistakes
Mistake: Confusing which axis is the y-axis and which is the x-axis.
Correction: Remember that the y-axis is vertical (up and down). A helpful trick: the letter "y" has a tail that hangs down, pointing along the vertical direction.
Mistake: Thinking a point like (3, 0) is on the y-axis.
Correction: A point is on the y-axis only when its x-coordinate is 0, such as (0, 3). The point (3, 0) is on the x-axis instead.