# GRAPHING LINEAR EQUATIONS IN TWO VARIABLES

## About "Graphing linear equations in two variables"

Graphing linear equations in two variables :

Graphing an equation which is in the form ax + by + c = 0 or y = mx + b is known as graphing linear equations in two variables.

To graph an equation which is in the form ax + by + c = 0, we need to know the following things

(i)  Slope of the line from the formula

m = -coefficient of y/coefficient of x

(ii) Find  x - intercept when y = 0

(iii)  Find y - intercept when x = 0

To graph an equation which is in the form y = mx + c, we need to know the following things

(i)  Slope of the line

m = coefficient of x

(ii) Find  x - intercept when y = 0

(iii)  y - intercept is c

Let us look into some examples to understand the above concept.

Example 1 :

Sketch the graph of the following line

7x - 2y - 2 = 0

Solution :

Step 1 :

Slope of the line 7x - 2y - 2 = 0

m = - coefficient of y/coefficient of x

m  =  -(-2)/7

m  =  2/7

Rise = 2 units and run = 7 units

Step 2 :

x - intercept when y = 0

7x - 2(0) - 2  =  0

7x - 2 = 0

7x = 2 ==> x  =  2/7 (x intercept)

Step 3 :

y - intercept when x = 0

7(0) - 2y - 2  =  0

2y - 2 = 0

2y = 2 ==> y  =  1 (y intercept) Example 2 :

Sketch the graph of the following line

x - 4y + 2 = 0

Solution :

Step 1 :

Slope of the line x - 4y + 2 = 0

m = - coefficient of y/coefficient of x

m  =  -(-4)/1

m  =  4/1

Rise = 4 units and run = 1 unit

Step 2 :

x - intercept when y = 0

x - 4(0) + 2  =  0

x + 2 = 0

x = -2 (x-intercept)

Step 3 :

y - intercept when x = 0

0 - 4y + 2  =  0

-4y + 2 = 0

4y = 2 ==> y  =  1/2 (y intercept) Example 3 :

Sketch the graph of the following line

y = 2x + 5

Solution :

Step 1 :

Slope of the line y = 2x + 5

m = coefficient of x

m  =  2

Rise = 2 units and run = 1 unit

Step 2 :

x - intercept when y = 0

y = 2x + 5

0 = 2x + 5

2x = -5

x = -5/2  ==>  -2.5 (x-intercept)

Step 3 :

y - intercept when x = 0

y = 2x + 5

y = 2(0) + 5

y = 5 (y-intercept) Example 4 :

Graph this line using the slope and y-intercept:

y = -6 x + 9

Solution :

Step 1 :

Slope of the line y = -6x + 9

m = coefficient of x

m  =  -6

Rise = 6 units and run = 1 unit

Step 2 :

x - intercept when y = 0

y = -6x + 9

0 = -6x + 9

6x = 9

x = 9/6  ==>  3/2 (x-intercept)

Step 3 :

y - intercept when x = 0

y = -6x + 9

y = -6(0) + 9

y = 9 (y-intercept)  After having gone through the stuff given above, we hope that the students would have understood "Graphing linear equations in two variables".

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