So far, all the equations that we have come across are linear in type. The most common difference between the two types of equations is as follows:

- A simple linear equation is of the form: y = mx + c
- A linear equation looks like a straight line when graphed.
- It has a constant slope value.
- The degree of a linear equation is always 1.
- Superposition principle is applicable to a system characterized by a linear equation.
- The output of a linear system is directly proportional to its input.

- A simple non-linear equation is of the form: ax
^{2}+ by^{2}= c - A non-linear equation look like a curve when graphed.
- It has a variable slope value.
- The degree of a non-linear equation is at least 2 or other higher integer values. With the increase in the degree of the equation, the curvature of the graph increases.
- Superposition principle does not apply to the systems characterized by non-linear equations.
- The input and output of a non-linear system is not directly related.

We have learned some techniques to solve linear equations. Solutions to non-linear equations are also possible, but they are comparatively difficult and more involved.

Next we discuss a few interesting things about equations. Kids your age might wonder as to how they can draw:

- A simple linear equation is of the form: y = mx + c
- A linear equation looks like a straight line when graphed.

on a piece of paper. We learn some easy ways to graph a linear equation in one or two variables.

Graphing an equation requires a co-ordinate plane. It consists of two straight lines one in
horizontal direction and the other in the vertical direction. The horizontal line is referred to
as **x-axis** and the vertical line is called **y-axis**. The point where the two lines
intersect is called **origin**.

A simple coordinate plane has been shown below.

There exist infinitely many points on the coordinate plane. A single point can be specified
with the help of two co-ordinate values x and y, and is represented in the form of an ordered
pair **(x,y)**. Here x and y can take any real value.

In order to graph a linear equation in one variable, we make use of a coordinate plane Let us present it through an example.

The given equation is

x – 3 = 0

x = 3

y+ 2 = 0

y = –2

This can be plotted on the coordinate plance as shown below.

Next we prsenet the graph of an equation in two variables.

This is easy and much similar to the above method of graphing. Let us present it through an example.

The given equation is y = 2x + 3. Since the equation has two variables x and y, we take two random values of x, and calculate the corresponding values of y by putting x into the equation.

Let us take x = 1 and x = –1.

x y

+1 2(+1) + 3 = 5

–1 2(–1) + 3 = 1

Now we plot the two points **(1,5)** and **(–1,1)** on the graph as shown in the figure
below.

Now you can simply join these two points by a straight line and that will give you the required graph of the given equation.

You can also varify that the graph obtained is a straight line by taking more than two points
and joining them as the equation is a first degree linear equation. The complete plot of the
graph using 5 points **(1,5)** , **(0,3)**, **(–1,1)**, **(–2, –1)**, **(–3, –3)** has been shown below which is a straight line as expected.

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