Write as a Function of y y^2=6x+4

$y^{2} = 6 x + 4$

Step 1

Rewrite the equation as $6 x + 4 = y^{2}$ .

$6 x + 4 = y^{2}$

Step 2

Subtract $4$ from both sides of the equation.

$6 x = y^{2} - 4$

Step 3

Divide each term in $6 x = y^{2} - 4$ by $6$ and simplify.

Divide each term in $6 x = y^{2} - 4$ by $6$ .

$\frac{6 x}{6} = \frac{y^{2}}{6} + \frac{- 4}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{y^{2}}{6} + \frac{- 4}{6}$

Divide $x$ by $1$ .

$x = \frac{y^{2}}{6} + \frac{- 4}{6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 4$ and $6$ .

Factor $2$ out of $- 4$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 4

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.

$f (y) = \frac{y^{2}}{6} - \frac{2}{3}$

Write as a Function of y y^2=6x+4

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