The 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).
The x-axis runs left and right. Points on it, like (−3, 0) and (4, 0), have a y-coordinate of 0. The x-coordinate of (3, 2) is the 3 you read on the x-axis.
Formal definition and notation
In the rectangular (Cartesian) coordinate system, the x-axis is the horizontal real number line through the origin, with positive numbers to the right. It is the set of all points (a, 0) and is the graph of the equation y = 0. Together with the perpendicular y-axis it divides the plane into four quadrants.
Symbol
Read it as
Meaning
(a, 0)
a comma zero
the form of every point on the x-axis
y = 0
y equals zero
the equation of the x-axis
x
x
the first coordinate in an ordered pair, measured along the x-axis
Key facts
The x-axis is horizontal, and the y-axis is vertical. They meet at a right angle at the origin.
Positive x-values are to the right of the origin; negative x-values are to the left.
Every point on the x-axis has y = 0, so the equation of the x-axis is y = 0.
Points on the x-axis are not in any quadrant; they lie on the border between quadrants.
Where a graph crosses the x-axis is its x-intercept; where it crosses the y-axis is its y-intercept.
Drag point A or B (or select one and use the arrow keys). Drop a point onto the green horizontal axis and the readout says it is on the x-axis: its y-coordinate becomes 0.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
X-Axis examples, step by step
Example 1: Which points are on the x-axis?
Warm-up
Which of these points lie on the x-axis: (0, 6), (−5, 0), (2, 2), (0, 0)?
A point is on the x-axis exactly when its y-coordinate (the second number) is 0.
(−5, 0) and (0, 0) have y = 0.
(0, 6) has x = 0, so it is on the y-axis instead; (2, 2) is in Quadrant I.
Answer: (−5, 0) and the origin (0, 0) lie on the x-axis.
Example 2: Where a line crosses the x-axis
Core
Where does the line 3x − 2y = 12 cross the x-axis?
A point is 3 units below the x-axis and 4 units to the left of the y-axis. What are its coordinates, and which quadrant is it in?
Distance from the y-axis sets the x-coordinate. Left means negative: x = −4.
Distance from the x-axis sets the y-coordinate. Below means negative: y = −3.
Write x first: (−4, −3). Both coordinates are negative, so the point is in Quadrant III.
Trap to avoid: 3 units below the x-axis is about y, not x.
Answer: The point is (−4, −3), in Quadrant III.
Common mistakes
✗ MistakeThe x-axis is the vertical line.
✓ InsteadThe x-axis is horizontal, and the y-axis is vertical.
A memory trick: the letter x is drawn across, like a horizon, and the x-axis runs left and right.
✗ Mistake(0, 5) is on the x-axis because it has a 0.
✓ Instead(0, 5) is on the y-axis. Points on the x-axis have y = 0, like (5, 0).
A zero x-coordinate means you never left the y-axis. A zero y-coordinate means you never left the x-axis.
✗ MistakeThe equation of the x-axis is x = 0.
✓ InsteadThe x-axis is y = 0. (x = 0 is the y-axis.)
An equation of a line describes what all its points share. Every point on the x-axis has a y-coordinate of 0.
Not to be confused with
X-Axisvs.Y-axis
The y-axis is the vertical number line; every point on it has x = 0, such as (0, −2). The x-axis is horizontal; every point on it has y = 0.
X-Axisvs.X-intercept
The x-axis is the whole horizontal line. An x-intercept is one point where a particular graph crosses it, such as (4, 0) for 3x − 2y = 12.
Quick check: 3 questions
Question 1 of 3
Which point lies on the x-axis?
Show answer and explanation
Answer: B. A point is on the x-axis when its y-coordinate is 0, so (−7, 0) is correct. Choice A has x = 0, which puts it on the y-axis; C and D are in Quadrants I and II.
Question 2 of 3
How far is the point (−6, 4) from the x-axis?
Show answer and explanation
Answer: A. Distance from the x-axis is the size of the y-coordinate: |4| = 4. Choice B is the distance from the y-axis, C adds the two, and a distance is never negative.
Question 3 of 3
Which equation is the x-axis?
Show answer and explanation
Answer: D. Every point on the x-axis has a y-coordinate of 0, so its equation is y = 0. Choice A is the y-axis, B is a diagonal line through the origin, and C is a vertical line.
X-Axis: frequently asked questions
Is the x-axis horizontal or vertical?
Horizontal. The x-axis runs left to right, and the y-axis runs up and down. To plot (x, y), move along the x-axis first (right if x is positive, left if negative), then up or down parallel to the y-axis. Alphabet order helps: x comes before y, and across comes before up.
What is the equation of the x-axis?
The x-axis is the line y = 0. Every point on it, such as (−3, 0), (0, 0) or (8, 0), has a y-coordinate of 0, and no point off the axis does. In the same way, the y-axis is the line x = 0. Students often swap these two, so check with one point.
What goes on the x-axis of a graph?
In a graph of real data, the x-axis usually shows the independent variable, the quantity you choose or that happens first, such as time, hours studied or temperature. The y-axis shows the dependent variable, the result. Always label each axis with the quantity and its units.
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 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 8NumberA 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 2Y-AxisThe 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).Geometry · Grade 5, Grade 6, Grade 7QuadrantA 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 7Ordered 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 4X-InterceptAn x-intercept is a point where a graph crosses or touches the x-axis. Its y-coordinate is always 0, so it is written (a, 0). To find it, set y = 0 and solve for x. A non-horizontal line has one x-intercept, while a parabola can have two, one or none.Algebra · Grade 8, Algebra 1, Algebra 2Y-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 1DataData 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 6Independent VariableAn independent variable is an input value that can be chosen or changed. The dependent variable changes based on it. In y = 3x, x is the independent variable and y is the dependent one. On a graph the independent variable goes on the horizontal axis; in an experiment it is the factor you change on purpose.Functions · Grade 6, Grade 7, Grade 8SubstituteSubstitute means to replace a variable with a number or with an equal expression. In 4x − 1, substituting 3 for x gives 4(3) − 1. You substitute to evaluate expressions, to check whether a number is a solution, and to solve systems of equations by swapping in an equal expression.Algebra · Grade 6, Grade 7, Grade 8SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6Number 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 6IntegerAn integer is a whole number, its opposite, or zero: the counting numbers, their negatives, and zero. The integers are …, −3, −2, −1, 0, 1, 2, 3, … and go on forever in both directions. Integers have no fractional or decimal part, so 4.5 and 12 are not integers.Number System · Grade 6, Grade 7, Grade 8SlopeSlope 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 7Scatter PlotA scatter plot displays paired numerical data as points on a coordinate plane, one point for each pair. It helps show whether two quantities have a pattern or relationship: points rising from left to right show a positive association, points falling show a negative association, and a shapeless cloud shows no association.Statistics · Grade 8, Algebra 1