WRITE LINEAR EQUATIONS IN STANDARD FORM

Standard Form of a Linear Equation

Ax + By  =  C

Example 1 :

Write the following linear equation in standard form.

y  =  3x + 1

Solution :

y  =  3x + 1

Subtract 3x from each side. 

-3x + y  =  1

Multiply each side by -1.

3x - y  =  -1

Example 2 :

Write the following linear equation in standard form.

y  =  x/2 - 3

Solution :

y  =  x/2 - 3

Multiply each side by 2.

2y  =  x - 6

Subtract x from each side. 

-x + 2y  =  -6

Multiply each side -1.

x - 2y  =  6

Example 3 :

Write the following linear equation in standard form.

y  =  1/4 - 7x/2

Solution :

y  =  1/4 - 7x/2

On the right side of the equation, we find the denominators 4 and 2. 

Find the least common multiple of 4 and 2 and multiply both sides of the equation by it to get rid of the denominators. 

Least common multiply of (4, 2) is 4.

Multiply each side of the above equation by 4. 

4y  =  1 - 14x

Add 14x to each side. 

14x + 4y  =  1

Example 4 :

Write the following linear equation in standard form.

y  =  -5x/4 + 1/6

Solution :

y  =  -5x/4 + 1/6

On the right side of the equation, we find the denominators  4 and 6. 

Find the least common multiple of 4 and 6 and multiply both sides of the equation by it to get rid of the denominators. 

Least common multiply of (4, 6) is 12.

Multiply each side of the above equation by 12. 

12y  =  -15x + 2

Add 15x to each side. 

15x + 12y  =  2

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