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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

**Method 1:**

**♦**** **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.

**Method 2:**

**♦ **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

**Example 1:**

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

There are two methods for graphing

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.

Draw a graph showing his wage.

The equation is y = 20x

X ( hours worked) | 0 | 1 | 2 | 3 |

Y ( wage in $) | 0 | 20 | 40 | 60 |