The y-axis is the up-and-down number line on the coordinate plane, with positive numbers above the origin and negative numbers below it. It meets the x-axis at the origin, (0, 0). A point’s y-coordinate is read along the y-axis, and every point on the y-axis has x-coordinate 0, like (0, 4).
Points on the y-axis, like (0, 4) and (0, −3), have x-coordinate 0. To read the y-coordinate of (−3, 2), slide straight across to the y-axis.
Formal definition and notation
In the rectangular coordinate system, the y-axis is the vertical real number line through the origin, perpendicular to the x-axis, with positive values upward. It is the set of all points (0, b) and is the graph of the equation x = 0. A graph crosses it at its y-intercept.
The y-axis is vertical; the x-axis is horizontal. They cross at a right angle at the origin.
Above the origin, y-values are positive; below it, they are negative.
The equation of the y-axis is x = 0, because every point on it has an x-coordinate of 0.
The y-intercept of a graph is where the graph crosses the y-axis; find it by setting x = 0.
Reflecting a point across the y-axis changes the sign of x only: (5, −3) becomes (−5, −3).
In a graph of data, the y-axis usually shows the dependent variable, the quantity being measured.
Try it: put a point on the y-axis
Interactive
Drag point A or B (or select it and use the arrow keys). Slide a point left or right until it sits on the vertical green axis: its x-coordinate becomes 0.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Y-Axis examples, step by step
Example 1: Which points are on the y-axis?
Warm-up
Which of these points lie on the y-axis: (3, 0), (0, −7), (1, 1), (0, 2)?
A point is on the y-axis exactly when its first number, x, is 0.
(0, −7) and (0, 2) have x = 0.
(3, 0) is on the x-axis instead, and (1, 1) is in Quadrant I.
Answer: (0, −7) and (0, 2) lie on the y-axis.
Example 2: Where a line crosses the y-axis
Core
Where does the line 2x + 5y = 15 cross the y-axis?
On the y-axis, x = 0: 2(0) + 5y = 15.
5y = 15, so y = 3.
Answer: It crosses the y-axis at (0, 3).
Example 3: Reflect across the y-axis
Test-style
Point P(5, −3) is reflected across the y-axis. What are the coordinates of its image, and how far is each point from the y-axis?
A reflection across the y-axis flips left and right, so x changes sign and y stays the same.
P′ = (−5, −3).
Distance from the y-axis is the size of x: both points are 5 units away, on opposite sides.
Trap: changing the sign of y gives (5, 3), which is a reflection across the x-axis.
Answer: The image is (−5, −3), and both points are 5 units from the y-axis.
Common mistakes
✗ MistakeThe y-axis runs left and right.
✓ InsteadThe y-axis runs up and down; the x-axis runs left and right.
In an ordered pair (x, y), you move along the x-axis first, then up or down along the y-axis.
✗ Mistake(4, 0) is on the y-axis because one coordinate is 0.
✓ Instead(4, 0) is on the x-axis. Points on the y-axis look like (0, 4).
x = 0 means no move left or right, so the point stays on the vertical axis.
✗ MistakeThe equation of the y-axis is y = 0.
✓ InsteadThe y-axis is x = 0; y = 0 is the x-axis.
An equation of a line states what all of its points share. All points on the y-axis share x = 0.
The y-axis is a whole line. The y-intercept is the one point where a given graph meets it, such as (0, 3) for 2x + 5y = 15.
Quick check: 3 questions
Question 1 of 3
Which point lies on the y-axis?
Show answer and explanation
Answer: C.(0, −6) has x = 0, so it is on the y-axis. Choice A has y = 0 (on the x-axis); B and D are in Quadrants IV and II.
Question 2 of 3
How far is (−7, 2) from the y-axis?
Show answer and explanation
Answer: B. Distance from the y-axis is the size of x: |−7| = 7. Choice A is the distance from the x-axis, C adds both, and distances are never negative.
Question 3 of 3
Which equation describes the y-axis?
Show answer and explanation
Answer: C. Every point on the y-axis has x-coordinate 0, so its equation is x = 0. y = 0 is the x-axis, y = x is a diagonal line, and y = 1 is horizontal.
Y-Axis: frequently asked questions
Is the y-axis vertical or horizontal?
Vertical. The y-axis runs straight up and down through the origin, with positive numbers above and negative numbers below. The x-axis is the horizontal one. To remember, think of an ordered pair (x, y): you walk along the floor first (x), then climb up or down (y).
What is on the y-axis of a graph?
In most graphs, the y-axis shows the dependent variable: the quantity that responds to the other one. On a graph of distance against time, for example, time goes on the x-axis and distance on the y-axis. Always read the axis label and its units before reading any value off the graph.
Coordinate PlaneThe coordinate plane is a flat grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin, (0, 0). Every point is located by an ordered pair, x first then y, such as (3, −2). The two axes divide the plane into four quadrants, numbered I to IV counterclockwise from the upper right.Geometry · Grade 5, Grade 6, Grade 7X-AxisThe x-axis is the horizontal number line on the coordinate plane. It crosses the vertical y-axis at the origin, (0, 0). The x-coordinate of a point tells how far to move along the x-axis, and every point on the x-axis has a y-coordinate of 0, such as (5, 0).Geometry · Grade 5, Grade 6, Grade 7Real NumberA real number is any number that can be placed on the number line. The real numbers are all the rational numbers (fractions, integers, terminating and repeating decimals) together with all the irrational numbers (such as √2 and π). Square roots of negative numbers, like √−4, are not real.Number System · Grade 8, Algebra 1OriginThe origin is the point where the x-axis and the y-axis cross on the coordinate plane. Its coordinates are (0, 0), and it is labeled O. Every ordered pair tells how far to move from the origin: (4, 3) means 4 units right, then 3 units up.Geometry · Grade 5, Grade 6, Grade 8Y-InterceptThe y-intercept is the point where a graph crosses the y-axis. Every point on the y-axis has x = 0, so you find the y-intercept by putting x = 0 into the equation. In y = mx + b, the y-intercept is b, written as the point (0, b).Algebra · Grade 8, Algebra 1NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Ordered PairAn ordered pair is two numbers written to locate a point on the coordinate plane. It is written as (x, y): the x-value comes first, and the y-value comes second. From the origin, move x units across, then y units up or down. The order matters: (2, 5) and (5, 2) are different points.Geometry · Grade 5, Grade 6, Grade 7Right AngleA right angle is an angle that measures exactly 90 degrees, a quarter of a full turn. It looks like the corner of a square or a sheet of paper, and it is marked with a small square at the vertex. Two lines that meet at a right angle are perpendicular.Geometry · Grade 2, Grade 3, Grade 4DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6Dependent VariableA dependent variable is the output value that changes based on the input. It responds to changes in the independent variable: in y = 2x + 1, y is the dependent variable because its value depends on x. On a graph it goes on the vertical axis, because its value depends on what the input was.Functions · Grade 6, Grade 7, Grade 8QuadrantA quadrant is one of the four regions that the x-axis and y-axis split the coordinate plane into. They are numbered I, II, III and IV counterclockwise, starting at the top right. The signs of a point’s coordinates tell its quadrant: (+, +) is I, (−, +) is II, (−, −) is III and (+, −) is IV.Geometry · Grade 5, Grade 6, Grade 7ReflectionA reflection is a transformation that flips a figure over a line to make a mirror image. That line is the line of reflection: each point and its image are the same distance from the line, on opposite sides. The image is congruent but faces the other way. Across the y-axis, (x, y) goes to (−x, y).Geometry · Grade 8, GeometrySideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2Negative NumberA negative number is a number less than zero, written with a minus sign, such as −3, −0.5 or −23. On a number line, negative numbers sit to the left of 0. They describe amounts below a starting point: temperatures below zero, depths below sea level, or money owed. Zero itself is neither negative nor positive.Number System · Grade 6, Grade 7Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6SlopeSlope is a number that measures how steep a line is: the change in y divided by the change in x between any two points on the line, often called rise over run. A positive slope rises from left to right, a negative slope falls, and a horizontal line has slope 0.Algebra · Grade 8, Algebra 1GraphA graph is a visual display of numbers, relationships, or data. Graphs help you see patterns, compare values, and understand relationships quickly. In algebra, the graph of an equation is the picture of all its solutions on a coordinate plane; in statistics, bar graphs, line graphs and scatter plots display data.Functions · Grade 5, Grade 6, Grade 7