Precalculus Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Divide $y$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $- 3$ by $3$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Cancel the common factor.

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

Step 6.1.1.1.2

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of $2$ .

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Step 6.1.1.2.1

Factor $2$ out of $2 k$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.2

Simplify the right side.

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Step 6.2.1

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

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Factor $2$ out of $- 2$ .

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

Step 6.2.1.1.2

Cancel the common factor.

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

Step 6.2.1.1.3

Rewrite the expression.

$k = 3 \cdot - 1$

Step 6.2.1.2

Multiply $3$ by $- 1$ .

$k = - 3$

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