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# Axis (Graph)|Definition & Meaning

**Definition**

Mathematics defines an axis as a line on which measurements can be made or marked. There are two lines in the coordinate plane that are important: the x-axis and the y-axis. Vertical numbers are represented by the y-axis and horizontal numbers are represented by the x-axis. The coordinate plane is formed by the intersection of these two axes perpendicularly. In coordinate pair (X,Y), X and Y are also referred to as abscissa and ordinate, respectively.

## Representation of X and Y Axis

The** two basic axes** can be represented by the following figure shown below. The **horizontal line** is making the **x-axis** (**horizontal axis**) which is shown by the red line while the **vertical line** is making the **y-axis** which is shown by the blue line (**vertical axis**). Whenever an **ordered pair** of points is written, the **x-axis** is **written first**. Each point on the graph has an ordered pair of x-coordinates leading to y-coordinates with the x-axis corresponding to a point on the graph.

## Structure of Coordinates on Axis

In** coordinate grids**, **points** are located by using** numbers**. There are two numbers that identify each point; **one number** on the **x-axis** and o**ne number** on the** y-axis**, called the **x-coordinate** and **y-coordinate**, respectively. It is common to read coordinates in **pairs (x, y)** in parentheses. In order to understand the **coordinate concept** we need to first define the following terms.

**Origin**

The **intersection** of the **x-axis and y-axis** is basically the origin which is usually highlighted by **“O”**.

**Abscissa**

Consider a point, Abscissa or x coordinate is its **distance** from the **y-axis** **with respect to** the **x-axis.**

**Ordinate**

Consider a point, Ordinate or y coordinate is its **distance** from the **x-axis with respect to** the **y-axis**.

All of the above concepts are illustrated in the figure shown below. **Point A** where **x=0 and y=0** or where the x and y axis **intersects** is referred to as **Origin**.While X and Y as **abscissa** and **ordinate** respectively.

## The Direction of Movements on Axes

**Positive X-Axis**

For the positive x-axis, we will move **horizontally** toward the **right side**.

**Negative X-Axis**

For the negative x-axis, we will move **horizontally** toward the **left side**.

**Positive Y-Axis**

For the positive Y-axis, we will move **vertically upward**

**Negative Y-Axis**

For Negative Y-axis, we will move **vertically downward**.

## Test Point Plotting on Axis

Consider a point **P(1,2),** below is the illustration of this point on axes. The x coordinate or **abscissa** is** “1”** and the y coordinate or **ordinate** is **“2”.**So what we will do is that starting from the origin as a reference we will move **1 step** right on the horizontal axis **(x-axis)** and we will move 2 steps upward on the vertical axis **(y-axis)**.

## Quadrants

X and Y axis **divide** the **coordinate plane** into **four** different **halves** which are referred to as **quadrants**. So there are four quadrants depending upon the positive and negative values of x and y. Below is the Illustration of Quadrants. The above figure shows the illustration of quadrants

**Quadrant 1**

The **top right portion** of the graph is known as the first quadrant. In this region the value of numbers lying on x and y on **both axes are positive**.

**Quadrant 2**

The **top left portion** of the graph is known as the second quadrant. In this region, the **value** of numbers lying on the** x-axi**s is **negative** while the **value** of numbers lying on the **y-axis** is **positive.**

**Quadrant 3**

The **bottom left portion** of the graph is known as the third quadrant. In this region, the **value** of numbers lying on the **x-axis** is **negative** while the **value** of numbers lying on the **y-axis** is also **negative**.

**Quadrant 4**

The **bottom right portion** of the graph is known as the fourth quadrant. In this region, the **value** of numbers lying on the **x-axis** is **positive** while the **value** of numbers lying on the** y-axis** is **negative**.

## Demonstrating Linearity Relation Between X and Y Axis

Consider the following equation

**Y = X+1**

Now we want to plot it on the x and y-axis. Let’s say we want to plot it for **four coordinate pairs**. Starting with the value of x from 0 to 3:

**X = 0**

Y = X+1

Y = 0+1

Y = 1

For x=0, we get **coordinate pair (0,1):**

**X = 1**

Y = X+1

Y =1 +1

Y = 2

For x=1, we get **coordinate pair (1,2):**

**X = 2**

Y = X+1

Y = 2+1

Y = 3

For x=2, we get **coordinate pair (2,3):**

**X = 3**

Y = 3+1

Y = 4

For x=3, we get **coordinate pair (3,4):**

Now we can see below illustration that there **exists** a **linear relationship** between the **x** and **y-axis**.

The coordinate pair **(0,1)** is shown by **point A**.

The coordinate pair **(1,2)** is shown by **point E**.

The coordinate pair **(2,3)** is shown by** point F**.

The coordinate pair **(3,4)** is shown by **point G**.

## An Example of Plotting on an Axis Graph

Consider the following coordinate pairs, **(2,3), (-3,2), (-1,-2)**, **plot** these points on the x-axis and y-axis, and also tell in **which quadrant** each coordinate pair lies. **Write** **abscissa** and **ordinate** each coordinate pair.

### Solution

Let **(2,3)** be the **first coordinate pair**, decomposing into abscissa and ordinate.

**Abscissa **= 2

**Ordinate **= 3

For plotting, We have to move **2 units** in a **horizontal direction** towards the **right** while we have to move **3 units** in a **vertical direction upward** with respect to the reference point that origin.

As** x is positive** and **y is also** positive so the point will lie in the** first quadrant** as we have seen previously that x-axis and y-axis are positive in the first quadrant. The illustration is shown in the above figure.

Let** (-3,2) b**e the **second coordinate pair,** decomposing into abscissa and ordinate.

**Abscissa **= -3

**Ordinate **= 2

For plotting, We have to move **3 units** in a **horizontal direction** towards the** left** while we have to move **2 units** in a **vertical** direction **upward** with respect to the reference point that origin.

As** x** is **negative** and** y** is **positive** so the point will lie in the **second quadrant** as we have seen previously the x-axis is negative and the y-axis is positive in the second quadrant. The illustration is shown in the above figure.

Let **(-1,-2)** be the **third coordinate pair**, decomposing into abscissa and ordinate.

**Abscissa **= -1

**Ordinate **= -2

For plotting, We have to move **1 unit** in a **horizontal** direction towards the **left** while we have to move **2 units** in a **vertical** direction d**ownward** with respect to the reference point that origin.

As **x** is **negative** and y is **negative** so the point will lie in the **third quadrant** as we have seen previously the x-axis and y-axis are negative in the third quadrant. The illustration is shown in the above figure.

*All mathematical drawings and images were created with GeoGebra.*