The term dependent and independent variable tells the relationship between two or more variable.

If the value of variable doesn’t depend on any other variable then it is** independent variable**.

On the other hand, if the value of one variable depends on the value of other variable then it is** dependent variable**.

## Examples of dependent and independent variables

(01) Let x and y are two variables, where;**x = side of square****y = area of square**

The formula for area of square is given as;

Area = side x side

\mathtt{y\ =\ x\times x}\\\ \\ \mathtt{y\ =\ x^{2}}

Note that as the side of square changes, the area variable (y) also change. **Hence, y is dependent variable** and **variable x is independent variable**.

(02) Let **” r be radius of circle** and **” A ” is area of circle**.

We know that;

Area of circle = \mathtt{\pi .r^{2}}

A = \mathtt{\pi .r^{2}}

Note that the value of variable “A” is dependent on variable ” r “. As the value of radius ” r” changes, the value of area “A” also changes.

Hence, **“r” is independent variable** and **” A ” is dependent variable**.

(03) Let **” x” be the quantity of diese**l in a car and **” y ” is the distance travelled**.

We know that more the quantity of diesel in the car, more distance it can travelled.

Since the value of “y” is dependent on “x”, we can say that **” y ” is dependent** and **“x ” is independent variable**.

### Graphical representation of dependent and independent variables

In cartesian planes, the value of **dependent variable is represented in y axis** and value of** independent variable is represented in x axis**.

i.e. Dependent variable ⟹ Y axis

Independent variable ⟹ X axis

Let us understand the graphical representation using example.

Let variable “x” is the side of square and variable ” y ” be area of square.

The formula for area of square is given as;

Area = side x side

\mathtt{y\ =\ x^{2}}

Generating some values for side and area.**Let x = 1 cm ;**

Then area will be given as;

\mathtt{y\ =\ 1^{2}}\\\ \\ \mathtt{y\ =\ 1\ cm^{2}}

**Let x = 2 cm;**

Calculating area, we get;

\mathtt{y\ =\ 2^{2}}\\\ \\ \mathtt{y\ =\ 4\ cm^{2}}

**Let x = 3 cm; **

Calculating area, we get;

\mathtt{y\ =\ 3^{2}}\\\ \\ \mathtt{y\ =\ 9\ cm^{2}}

Now plotting the independent variable on x axis and dependent variable on y axis.

One can infer following information from above graph.

Point (1, 1) tells following information;

Side of square is 1 cm.

Area of square is 1 sq. cm.

Point (2, 4) gives following information;

Side of square is 2 cm.

Area of square is 4 cm.

Point (3, 9) gives following information;

Side of square is 3 cm.

Area of square is 9 cm.

## Dependent and Independent variables – Solved examples

(01) Among the given variables,** identify the independent and dependent variables**.

(i) John works in a restaurant.

A = Number of work hours

B = Daily earning.

(ii) Diana owns a hotel. The two variables related to hotel business is given as;

A = Number of people that can sleep

B = number of beds in hotel

(iii) Kirsten wants to go shopping but she is confused about relation between following variables;

(A) Amount of money in hand

(B) Number of items that can be purchased

(IV) Daniel and Annie are planning their wedding and they want to understand the relation between following variables;

(A) Number of invitation

(B)number of guest turnout

**Solution**

(i) A = Number of work hours

B = Daily earning.

The more hours John works, the more earning he will have after complete day.

Hence his earning is dependent on number of work hours.

So **” A” is independent and B is dependent variable.**

(ii) A = Number of people that can sleep

B = number of beds in hotel

More the number of beds, more people can sleep there.

So, **“B” is independent variable and “A” is dependent variable**.

(iii) A= Amount of money in hand

B = Number of items that can be purchased

More money you have, more item you can purchase.**“A” is independent variable and “B” is dependent variable.**

(iv) A = Number of invitation

B = number of guest turnout

The more invitation you give, the more people will come to our wedding.**So, “A” is independent and “B” is dependent variable.**