X and Y Axis

X and Y Axis are the foundation of the Cartesian coordinate system as well as graphs in mathematics. The x-axis and y-axis are crucial components of the coordinate plane, with the x-axis serving as a horizontal number line and the y-axis as a vertical number line. The x-axis is referred to as the abscissa, while the y-axis is known as the ordinate.

They intersect at right angles to create the coordinate plane. The point where the X and Y axis intersect is called the origin and is represented by the coordinates (0, 0) i.e. , the intersection of the X and Y axis.

What is X-Axis?

The Horizontal line that divides the cartesian plane into two equal parts is called the x-axis various properties of the x-axis are,

• X axis is the horizontal line on a graph or coordinate plane.
• The X-axis is used to represent the variable(x) in the graph.
• Any point on the x-axis has 0 as its y-coordinate.
• The equation of the x-axis is, y = 0

Positive and Negative X-Axis

The X axis is a horizontal line that runs from left to right on the Cartesian plane. The right-hand side of the origin is considered the positive X axis (+X), while the left-hand side is the negative X axis (-X). The X axis divides the plane into two halves, known as quadrant

Points on X Axis

All points on the X axis have a Y-coordinate of zero since they lie on a horizontal line. These points are represented in the form of (x, 0), where x is the X-coordinate. Equation of X Axis

Equation of X-Axis

The equation of the X axis is simply y = 0, where y represents the Y-coordinate. This equation indicates that all the points on the X axis have a Y-coordinate of zero.

What is Y-Axis?

The Horizontal line that divides the cartesian plane into two equal parts is called the x-axis various properties of the x-axis are,

• Y axis is the vertical line on a graph or cartesian plane.
• It is used to represent the variable(y) in the graph.
• Any point on the y-axis has 0 as its x coordinate.
• Equation of y-axis is, x = 0

Positive and Negative Y-Axis

The Y axis extends upward from the origin, and all points on this axis have a positive Y-coordinate. Conversely, it extends downward, and points on this side have a negative Y-coordinate. The positive direction is usually denoted as the upward direction, and the negative direction is denoted as the downward direction.

Points on Y Axis

All points on the Y axis have an X-coordinate of zero since they lie on a vertical line. These points are represented in the form of (0, y), where y is the Y-coordinate.

Equation of Y Axis

The equation of the Y axis is simply x = 0, where x represents the X-coordinate. This equation indicates that all the points on the Y axis have an X-coordinate of zero.

Learn More: Coordinate Axes and Coordinate Planes in 3D.

X and Y Axis on Graph

When the X and Y axes are combined, they form a grid known as the Cartesian Plane or the XY plane. This plane is divided into four quadrants, each designated by Roman numerals I, II, III, and IV. Quadrant I is in the upper right, Quadrant II is in the upper left, Quadrant III is in the lower left, and Quadrant IV is in the lower right.

Plotting Points on X and Y Axis

To determine any point on the coordinate plane, we apply an ordered pair where the ordered pair is formulated as (x-coordinate, y-coordinate)/(x, y). Here the x-coordinate denotes a point on the x-axes which is the perpendicular distance from the y-axes and the y-coordinate denotes a point on the y-axes that is the perpendicular distance from the x-axes, therefore it is obvious from above that x-axis comes first when addressing the ordered pair to locate a point.

Axis and Quadrants of Cartesian Plane

The X and Y axes divide the Cartesian Plane into four quadrants, each with unique characteristics.

• Quadrant I contain points with both positive X and Y coordinates.
• Quadrant II contains points with negative X and positive Y coordinates.
• Quadrant III contains points with negative X and Y coordinates.
• Quadrant IV contains points with positive X and negative Y coordinates.

People Also Read:

• Coordinate Geometry
• Parallel Lines
• Distance Formula

Solved Examples X and Y Axes

Problem 1: Plott the given points on the cartesian plane.

• A: (2, 3)
• B: (-1, 4)
• C: (0, -2)
• D: (-3, -4)
• E: (6, -5)

Solution:

Given Points,

• Point A: (2, 3)
• Point B: (-1, 4)
• Point C: (0, -2)
• Point D: (-3, -4)
• Point E: (6, -5)

To plot these points on the coordinate plane, start at the origin (0, 0) and move horizontally and vertically according to the X and Y values of each point.

• For Point A (2, 3), move two units to the right along the X-axis and three units upward along the Y-axis to locate the point.
• For Point B (-1, 4), move one unit to the left along the X-axis and four units upward along the Y-axis.
• For Point C (0, -2), stay at the origin and move two units downward along the Y-axis.
• Point D (-3, -4), move 3 units to the left along the X-axis and 4 units downwards along the Y-axis from the origin locate the point.
• Point E (6, -5), move 6 units to the right along the X-axis and 5 units downwards along the Y-axis from the origin locate the point.

Now, let's graph these points on the coordinate plane. The resulting graph will show the positions of these points relative to the origin.

👁 Points-in-Cartesian-Plane

Problem 2: Plot a graph of the linear equation y = 2x + 1
Solution:

Given equation,

y = 2x + 1

To graph this linear equation, we need to find several points that satisfy the equation and then connect them to form a line. We can choose any X value and find the corresponding Y value using the equation.

Let's calculate y for different values of x,

• When x = 0

y = 2(0) + 1

y = 1

So, the point (0, 1) lies on the line.

• When x = 1

y = 2(1) + 1

y = 3

So, the point (1, 3) lies on the line.

• When x = -1

y = 2(-1) + 1

y = -1

So, the point (-1, -1) lies on the line.

Now, plot these points on the coordinate plane and connect them to form a straight line. The graph of the linear equation y = 2x + 1 will look like this:

👁 Line-in-Cartesian-Plane-min