Algebra Examples

$3 y = 2 k x - 3$ , $m = - 2$

Divide each term by $3$ and simplify.

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Divide each term in $3 y = 2 k x - 3$ by $3$ .

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Divide $- 3$ by $3$ .

$y = \frac{2 k x}{3} - 1$

Find slope of the equation in terms of $k$ using the slope-intercept form.

$m = \frac{2 k}{3}$

Set the known value of $m$ equal to the slope of the equation in terms of $k$ .

$- 2 = \frac{2 k}{3}$

Rewrite the equation as $\frac{2 k}{3} = - 2$ .

$\frac{2 k}{3} = - 2$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 k}{3} = \frac{3}{2} \cdot - 2$

Simplify both sides of the equation.

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Simplify the left side.

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Cancel the common factor of $3$ .

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Factor out the greatest common factor $3$ .

$\frac{3 \cdot 1}{2} \cdot \frac{2 k}{3 \cdot 1} = \frac{3}{2} \cdot - 2$

Cancel the common factor.

$\frac{3 \cdot 1}{2} \cdot \frac{2 k}{3 \cdot 1} = \frac{3}{2} \cdot - 2$

Rewrite the expression.

$\frac{1}{2} \cdot \frac{2 k}{1} = \frac{3}{2} \cdot - 2$

Cancel the common factor of $2$ .

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Factor out the greatest common factor $2$ .

$\frac{1}{2 (1)} \cdot \frac{2 (k)}{1} = \frac{3}{2} \cdot - 2$

Cancel the common factor.

$\frac{1}{2 \cdot 1} \cdot \frac{2 k}{1} = \frac{3}{2} \cdot - 2$

Rewrite the expression.

$\frac{1}{1} \cdot \frac{k}{1} = \frac{3}{2} \cdot - 2$

Simplify.

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Multiply $\frac{1}{1}$ and $\frac{k}{1}$ .

$\frac{k}{1} = \frac{3}{2} \cdot - 2$

Divide $k$ by $1$ .

$k = \frac{3}{2} \cdot - 2$

Simplify $\frac{3}{2} \cdot - 2$ .

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Multiply $\frac{3}{2} \cdot - 2$ .

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

$k = \frac{3 \cdot - 2}{2}$

Multiply $3$ by $- 2$ .

$k = \frac{- 6}{2}$

Divide $- 6$ by $2$ .

$k = - 3$

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