
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:
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:
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.
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.
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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