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Examples

y = \frac{6}{8} x^{2}

$y = \frac{6}{8} x^{2}$

Step 1

Simplify

\frac{6}{8} x^{2}

$\frac{6}{8} x^{2}$ .

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Step 1.1

Cancel the common factor of

6

$6$ and

8

$8$ .

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Step 1.1.1

Factor

2

$2$ out of

6

$6$ .

y = \frac{2 (3)}{8} x^{2}

$y = \frac{2 (3)}{8} x^{2}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor

2

$2$ out of

8

$8$ .

y = \frac{2 \cdot 3}{2 \cdot 4} x^{2}

$y = \frac{2 \cdot 3}{2 \cdot 4} x^{2}$

Step 1.1.2.2

Cancel the common factor.

y = \frac{2 \cdot 3}{2 \cdot 4} x^{2}

$y = \frac{2 \cdot 3}{2 \cdot 4} x^{2}$

Step 1.1.2.3

Rewrite the expression.

y = \frac{3}{4} x^{2}

$y = \frac{3}{4} x^{2}$

y = \frac{3}{4} x^{2}

$y = \frac{3}{4} x^{2}$

y = \frac{3}{4} x^{2}

$y = \frac{3}{4} x^{2}$

Step 1.2

Combine

\frac{3}{4}

$\frac{3}{4}$ and

x^{2}

$x^{2}$ .

y = \frac{3 x^{2}}{4}

$y = \frac{3 x^{2}}{4}$

y = \frac{3 x^{2}}{4}

$y = \frac{3 x^{2}}{4}$

Step 2

Since the equation can be written in the form

y = k x^{2}

$y = k x^{2}$ ,

y

$y$ varies directly with

x^{2}

$x^{2}$ and

k

$k$ . The constant of variation,

k

$k$ , is

\frac{3}{4}

$\frac{3}{4}$ .

\frac{3}{4}

$\frac{3}{4}$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$