Precalculus Examples

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

Step 1

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

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Step 1.1

Cancel the common factor of $6$ and $9$ .

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Step 1.1.1

Factor $3$ out of $6$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $9$ .

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

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.

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

Step 1.2

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

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

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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