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

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

Step 1

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

Step 2

Multiply both sides by $3$ .

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

Step 3

Simplify the left side.

Simplify $3 (2 y + 3)$ .

Apply the distributive property.

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

Multiply.

Multiply $2$ by $3$ .

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

Multiply $3$ by $3$ .

$6 y + 9 = 3 (- \frac{1}{3} (x - 2))$

Step 4

Simplify the right side.

Simplify $3 (- \frac{1}{3} (x - 2))$ .

Apply the distributive property.

$6 y + 9 = 3 (- \frac{1}{3} x - \frac{1}{3} \cdot - 2)$

Combine $x$ and $\frac{1}{3}$ .

$6 y + 9 = 3 (- \frac{x}{3} - \frac{1}{3} \cdot - 2)$

Multiply $- \frac{1}{3} \cdot - 2$ .

Multiply $- 2$ by $- 1$ .

$6 y + 9 = 3 (- \frac{x}{3} + 2 (\frac{1}{3}))$

Combine $2$ and $\frac{1}{3}$ .

$6 y + 9 = 3 (- \frac{x}{3} + \frac{2}{3})$

Apply the distributive property.

$6 y + 9 = 3 (- \frac{x}{3}) + 3 (\frac{2}{3})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$6 y + 9 = 3 \frac{- x}{3} + 3 (\frac{2}{3})$

Cancel the common factor.

$6 y + 9 = 3 \frac{- x}{3} + 3 (\frac{2}{3})$

Rewrite the expression.

$6 y + 9 = - x + 3 (\frac{2}{3})$

Cancel the common factor of $3$ .

Cancel the common factor.

$6 y + 9 = - x + 3 (\frac{2}{3})$

Rewrite the expression.

$6 y + 9 = - x + 2$

Step 5

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

Add $x$ to both sides of the equation.

$6 y + 9 + x = 2$

Move $9$ .

$6 y + x + 9 = 2$

Reorder $6 y$ and $x$ .

$x + 6 y + 9 = 2$

Step 6

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

Subtract $9$ from both sides of the equation.

$x + 6 y = 2 - 9$

Subtract $9$ from $2$ .

$x + 6 y = - 7$

Step 7

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

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