Precalculus Examples

$3 y - 6 = k x$ , $m = 3$

Step 1

Add $6$ to both sides of the equation.

$3 y = k x + 6$

Step 2

Divide each term in $3 y = k x + 6$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 y = k x + 6$ by $3$ .

$\frac{3 y}{3} = \frac{k x}{3} + \frac{6}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{k x}{3} + \frac{6}{3}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{k x}{3} + \frac{6}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $6$ by $3$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Multiply both sides of the equation by $3$ .

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

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Cancel the common factor of $3$ .

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Step 7.1.1.1

Cancel the common factor.

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

Step 7.1.1.2

Rewrite the expression.

$k = 3 \cdot 3$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $3$ by $3$ .

$k = 9$

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