Linear Equations

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:


 Types Of Equations

Linear Equations

  •  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.

Non-Linear Equations

  •  A simple non-linear equation is of the form: ax2 + by2 = 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.


Some interesting Topics related to Equations:


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 a linear equation in one variable:


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.


One Variable Linear Equation Graph

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.


PPT of how to solve equations


Simultaneous equations from ipracticemath

Linear Equation on Graph Examples


Explanation:

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.


One Variable Linear Equation Graph


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

Graphing a linear equation in two variables:

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


Linear Equation on a Coordinate Plane Example


Explanation:

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.


Two Variable Linear Equation Graph


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.


Two Variable Linear Equation Graph







Become a member today (it’s Free)!


 Register with us

Are you a member? Sign in!


 Login to your account