# Graph of standard linear relation between x & y

In this chapter, we will plot graph of common function between variable x and y.

Try to remember each of the given graph as the question related to it is directly asked in competition exams.

(i) x = 0

It is a graph in which the value of x is 0 at any given point.

Some of the coordinates for this function is given below.
(-1, 0), (0, 0), (0, 1), (0, 2), (0, 3) etc.

Plot any three points on the graph and join it with the straight line.

Given below is the graph of function x = 0.

Note that the graph of function x = 0 is simply a vertical y axis line.

(ii) y = 0

This is function in which for all value of x, the value of y is zero.

Given below are some coordinate points for this function.
(-1,0), (1, 0), (2, 0), (3, 0), (4, 0) etc.

Plot any three points on the graph and join it with the straight line.

Given below is the graph of function y = 0.

Note that the graph of function y = 0 is a straight horizontal x axis line.

(iii) x = k

The function states that for any value of y, the value of x will remain the same constant k.

Suppose the value of constant k = 4, then the possible coordinates for this function is given below;
( 4, -1), (4, 0), (4, 1), (4, 2), (4, 3) etc..

To plot the above function, locate three of the above points in the graph and join it with the straight line.

The graph of function x = 4 is a straight line parallel to y axis in which all the value of x coordinate is 4.

The distance of the line from y axis depend on the value of constant k.

In the above example, the value of k is 4. That’s why the line is located 4 unit distance from y axis.

Conclusion
The graph of x = k will always be straight line parallel to y axis, located at distance k from the y axis.

(iv) y = k

The function tells that for all value of x, the value of y coordinate will be constant.

Let the value of k = 5.
Then the possible coordinates are given below;
(-1, 5), (0, 5), (1, 5), (2, 5), (3, 5) etc..

To plot the graph of y = 5, locate the above three points and join them with the straight line.

Note that the graph of y = 5 is a straight horizontal line parallel to x axis.

The distance of line from x axis depend on the value of constant x.

In the above example, the value of k = 5. That’s why the line is located 5 unit distance from x axis.

Conclusion
The graph of function y = k will be horizontal line parallel to x axis.

(v) x = y

The above expression tells that it is a function in which value of x coordinate is equal to y coordinate.

Some points related to the function is given below;
(-2, -2), (-1,-1), (0, 0), (1, 1), (2, 2), (3, 3) etc..

To plot the graph, locate any three points and join them with straight line.

Given above is the graph of function x = y.

Note that the graph is a straight line making 45 degree angle with positive x axis.

(vi) Graph of linear expression, x + y = 5

To plot the graph of above expression, you have to find at-least three coordinate points.

Put x = 1 in the given equation.

1 + y = 5

y = 4

So we get point (1, 4).

Now put x = 2;

2 + y = 5

y = 5 – 2

y = 3

We get the point (2, 3).

Now put x = 3,

3 + y = 5

y = 5 – 3

y = 2

We get the point (3, 2).

Locate these three points (1, 4), (2, 3) and (3, 2) on the graph and join them with straight line.

On joining the points, you get a straight line.

The above process is similar for any given linear expression and you will always get the straight line.