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Precalculus Examples

y = \frac{6}{9} x

$y = \frac{6}{9} x$

Step 1

Simplify

\frac{6}{9} x

$\frac{6}{9} x$ .

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Step 1.1

Cancel the common factor of

6

$6$ and

9

$9$ .

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Step 1.1.1

Factor

3

$3$ out of

6

$6$ .

y = \frac{3 (2)}{9} x

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor

3

$3$ out of

9

$9$ .

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

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

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

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

Step 1.2

Combine

$\frac{2}{3}$ and

$x$ .

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

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

Step 2

Since the equation can be written in the form

$y = k x$ ,

$y$ varies directly with

$x$ and

$k$ . The constant of variation,

$k$ , is

$\frac{2}{3}$ .

$\frac{2}{3}$

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