**Independent variables:**

We know that the variable is thing that can be vary according to some conditions or the nature of the function. In this the variable does not depends on any variable and that can be
predetermined for calculate the **dependent variable** . The dependent variable can be changeable according to the independent variable.For example y = 3x + 5. Here x is independent
variable and y is dependent variable.

The axis of an independent variable in a graph is x axis. The dependent variable is plotted on y axis.

**Graph:**

The diagrammatic representation of the set of data is known as graph. The graph contains x and y axis in two dimensional graph. In a three dimensional, there are three axis named as x axis, y axis, z axis.

In this article we are going to see about independent variable on graph.

**Problem 1:**

Draw the graph of the independent variable y = 3x + 9 when y =0.

**Solution:**

Given, y = 3x + 9

We need to draw the graph of the function y = 3x + 9 , when y = 0.

Here the variable y is dependent on the variable x.

Substitute y = 0 in the above equation to draw the independent variable graph on x axis.

y = 3x + 9

0 = 3x + 9

Subtract 9 on both sides,

0 - 9 = 3x + 9 - 9

-9 = 3x

3x = -9

Divided by 3 on both sides,

3x / 3 = -9 / 3

x = -3

**Graph:**

**Problem 2:**

Draw the graph of the function y = (x - 2)^2 when y = 0

**Solution:**

Given y = (x - 2)^2

We need to draw the graph of the function y = (x - 2)^2 , when y = 0.

Here the variable y is dependent on the variable x.

Substitute y = 0 in the above equation to draw the independent variable graph on x axis.

y = (x - 2)^2

0 = (x - 2)^2

(x - 2)^2 = 0

(x - 2) ( x - 2) = 0

x - 2 = 0 and x - 2 = 0

Add 2 on both sides,

x = 2 , x = 2

**Graph:**

**Problems :**

1. Draw the graph of x = -9

2. Draw the graph of x = 24