Write as a Function of y 6x-3y=2

$6 x - 3 y = 2$

Step 1

Add $3 y$ to both sides of the equation.

$6 x = 2 + 3 y$

Step 2

Divide each term in $6 x = 2 + 3 y$ by $6$ and simplify.

Divide each term in $6 x = 2 + 3 y$ by $6$ .

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{1}{3} + \frac{3 y}{6}$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3 y$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

To rewrite as a function of $y$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $y$ is on the other side.

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

Write as a Function of y 6x-3y=2

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