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 $1$ to get $y$ .

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

Simplify each term.

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Divide $3$ by $3$ to get $1$ .

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

Multiply $- 1$ by $1$ to get $- 1$ .

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

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

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

Solve for $k$ .

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Multiply both sides of the equation by $3$ .

$2 k = - 2 \cdot 3$

Multiply $- 2$ by $3$ to get $- 6$ .

$2 k = - 6$

Divide each term by $2$ and simplify.

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Divide each term in $2 k = - 6$ by $2$ .

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $k$ by $1$ to get $k$ .

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

Simplify the right side of the equation.

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Divide $6$ by $2$ to get $3$ .

$k = - 1 \cdot 3$

Multiply $- 1$ by $3$ to get $- 3$ .

$k = - 3$

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