Algebra Examples

3 y = 2 x

$3 y = 2 x$

Step 1

Divide each term in

3 y = 2 x

$3 y = 2 x$ by

3

$3$ and simplify.

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Step 1.1

Divide each term in

3 y = 2 x

$3 y = 2 x$ by

3

$3$ .

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

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of

3

$3$ .

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Step 1.2.1.1

Cancel the common factor.

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

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

Step 1.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{2 x}{3}

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

y = \frac{2 x}{3}

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

y = \frac{2 x}{3}

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

y = \frac{2 x}{3}

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

Step 2

Since the equation can be written in the form

y = k x

$y = k x$ ,

y

$y$ varies directly with

x

$x$ and

k

$k$ . The constant of variation,

k

$k$ , is

\frac{2}{3}

$\frac{2}{3}$ .

\frac{2}{3}

$\frac{2}{3}$

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

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