Write in Standard Form y-3=1/2(x+6)

$y - 3 = \frac{1}{2} (x + 6)$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $2$ .

$2 (y - 3) = 2 (\frac{1}{2} (x + 6))$

Step 3

Simplify the left side.

Simplify $2 (y - 3)$ .

Apply the distributive property.

$2 y + 2 \cdot - 3 = 2 (\frac{1}{2} (x + 6))$

Multiply $2$ by $- 3$ .

$2 y - 6 = 2 (\frac{1}{2} (x + 6))$

Step 4

Simplify the right side.

Simplify $2 (\frac{1}{2} (x + 6))$ .

Apply the distributive property.

$2 y - 6 = 2 (\frac{1}{2} x + \frac{1}{2} \cdot 6)$

Combine $\frac{1}{2}$ and $x$ .

$2 y - 6 = 2 (\frac{x}{2} + \frac{1}{2} \cdot 6)$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 y - 6 = 2 (\frac{x}{2} + \frac{1}{2} \cdot (2 (3)))$

Cancel the common factor.

$2 y - 6 = 2 (\frac{x}{2} + \frac{1}{2} \cdot (2 \cdot 3))$

Rewrite the expression.

$2 y - 6 = 2 (\frac{x}{2} + 3)$

Apply the distributive property.

$2 y - 6 = 2 \frac{x}{2} + 2 \cdot 3$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 y - 6 = 2 \frac{x}{2} + 2 \cdot 3$

Rewrite the expression.

$2 y - 6 = x + 2 \cdot 3$

Multiply $2$ by $3$ .

$2 y - 6 = x + 6$

Step 5

Rewrite the equation.

$x + 6 = 2 y - 6$

Step 6

Move all terms containing variables to the left side of the equation.

Subtract $2 y$ from both sides of the equation.

$x + 6 - 2 y = - 6$

Move $6$ .

$x - 2 y + 6 = - 6$

Step 7

Move all terms not containing a variable to the right side of the equation.

Subtract $6$ from both sides of the equation.

$x - 2 y = - 6 - 6$

Subtract $6$ from $- 6$ .

$x - 2 y = - 12$

Step 8

Write in Standard Form y-3=1/2(x+6)

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