Draw the following graphs:
y = x, y = 2x, y = (1/2)x and y = (1/3)x.
In the above problems to find y value we can take any value for x, but our
convenience we are taking only integers.
The ordered pairs for the graph y = x
x  2  1  1  2 
y = x  2  1  1  2 
Ordered pairs  (2,2)  (1,1)  (1,1)  (2,2) 
The ordered pairs for the graph y = 2x
x  2  1  1  2 
y = 2x  4  2  2  4 
Ordered pairs  (2,4)  (1,2)  (1,2)  (2,4) 
The ordered pairs for the graph y = (1/2)x
x  4  2  2  4 
y = (1/2)x  2  1  1  2 
Ordered pairs  (4,2)  (2,1)  (2,1)  (4,2) 
The ordered pairs for the graph y = (1/3)x
x  6  3  3  6 
y = (1/3)x  2  1  1  2 
Ordered pairs  (6,2)  (3,1)  (3,1)  (6,2) 
Observing above graphs:
1. All these lines are passing through the origin.
2. All these lines are passing through II and IV quadrants.
3. The general form of these lines are y = mx, where m = 1/3, 1/2, 1 and 2.
4. For negative value of m that is the coefficient of x is negative and the graph slopes upwards to left, as the value of m
decreases the line move towards Yaxis.
5. In y = mx, m is known as the slope and m is the coefficient of x.
6. m = y/m, that is slope is the ratio between ycoordinate and xcoordinate.
For any m Î R, y = mx is a straight line and passes through the origin. 
Directions: Draw the graph for y = 3x, y = 4x, y = (1/4)x and y = (1/5)x
