A pictorial representation which explains the relationship between x and y is called a graph for those variables. In case of a simultaneous linear equation in x and y the graph is a straight line. The set of points whose coordinates satisfy this equation will form the required straight line.
There are two methods for graphing
♦ The equation in the standard form is written as y = m x + b where m is the slope of the line and b is the y intercept which is a point on y axis.
♦ Y intercept is placed in the coordinate system
♦ Starting from y intercept and using the slope we locate one more point on the coordinate system.
♦ We draw a line between the y intercept and the other point.
♦ We can find the coordinates of any three points on the given line by giving arbitrary values to x and then using the equation to find corresponding y values.
♦ Then we plot the set of points on the graph
The points (3, -1) , (2, -3), ( 0 , -7) , (3.5 ,0 ) all lie on the graph of 2x – y = 7 because they satisfy the equation.
Example 2:John earns $20 per hour. How much does he earn working 3 hours?
Draw a graph showing his wage.
Solution: Let x be the number of hours worked ,y be wages
The equation is y = 20x
X ( hours worked)
Y ( wage in $)