# WRITE EQUATIONS IN STANDARD FORM

## About "Write equations in standard form"

Write equations in standard form :

Standard form of the equation is ax + by = c, where a, b and c are integers.

Now let us look into some example problems to understand how to convert the given equation into standard form.

Example 1 :

Write the following equation in standard form using integers

y = 3x + 1

Solution :

Here the above given equation is in slope intercept form (y = mx +b).

In order to convert it into standard form, we have to bring x and y terms on the left side of the equal sign and constant to the the right side.

y = 3x + 1

Subtract 3x from both sides

y - 3x  = 3x - 3x + 1

-3x + y  =  1

Multiply negative sign to both sides

-(-3x + y)  =  -1

3x - y = -1

Example 2 :

Write the following equation in standard form using integers

y = (1/2)x - 3

Solution :

y = (x/2) - (3/1)

Take L.C.M to the right side

y = (x/2) - (3/1) (2/2)

y = (x - 3)/2

Multiply both sides by 2.

2y = x - 3

Subtract both sides by 2y

2y -2y = x - 2y - 3

0 = x - 2y - 3

0 + 3 = x - 2y + 3

3 = x - 2y

x - 2y = 3

Example 3 :

Write the following equation in standard form using integers

y = (7x/2) + (1/4)

Solution :

y = (7x/2) + (1/4)

Take L.C.M to the right side

y = (7x/2) (2/2) - (1/4)

y = (14x/4) - (1/4)

y = (14x - 1)/4

Multiply both sides by 4.

4y = 14x - 1

Subtract both sides by 4y

4y - 4y = 14x - 4y - 1

0 = 14x - 4y - 1

0 + 1 = 14x - 4y - 1 + 1

1 = 14x - 4y

14x - 4y = 1

Example 4 :

Write the following equation in standard form using integers

y = (-2x/5) + (1/10)

Solution :

y = (-2x/5) + (1/10)

Take L.C.M to the right side

y = (-2x/5) (2/2) + (1/10)

y = (-4x/10) + (1/10)

y = (-4x + 1)/10

Multiply both sides by 10.

10y = -4x + 1

10y + 4x = -4x + 4x + 1

10y + 4x = 1

4x + 10y = 1

After having gone through the stuff given above, we hope that the students would have understood, "Write equations in standard form".

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