CONVERTING SLOPE INTERCEPT FORM TO STANDARD FORM

In this section, you will learn how to convert a linear equation in slope-intercept form to standard form.

Slope intercept form

Standard form

y = mx + b

ax + by = c

Example 1 :

Write the following slope-intercept form equation of a line 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 slope-intercept form equation of a line 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 by -1.

x - 2y = 6

Example 3 :

Write the following slope-intercept form equation of a line in standard form :

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

Solution :

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

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

Least common multiple of (2 and 4) is 4.

Multiply both sides of the equation by 4 to get rid of the denominators 2 and 4.

4y = 14x + 1

Subtract 14x from each side.

-14x + 4y = 1

Multiply each side by -1.

14x - 4y = -1

Example 4 :

Write the following slope-intercept form equation of a line in standard form :

y = (-5x/6) + (1/4)

Solution :

y = (-5x/4) + (1/6)

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

Least common multiple of (4 and 6) is 12.

Multiply both sides of the equation by 12 to get rid of the denominators 4 and 6.

12y = -15x + 2

Add 15x to each side.

15x + 12y = 2

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