Precalculus Examples

$6 x = 3 y - 9$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Rewrite the equation as $3 y - 9 = 6 x$ .

$3 y - 9 = 6 x$

Step 1.3

Add $9$ to both sides of the equation.

$3 y = 6 x + 9$

Step 1.4

Divide each term in $3 y = 6 x + 9$ by $3$ and simplify.

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Step 1.4.1

Divide each term in $3 y = 6 x + 9$ by $3$ .

$\frac{3 y}{3} = \frac{6 x}{3} + \frac{9}{3}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $3$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{6 x}{3} + \frac{9}{3}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{3} + \frac{9}{3}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Cancel the common factor of $6$ and $3$ .

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Step 1.4.3.1.1.1

Factor $3$ out of $6 x$ .

$y = \frac{3 (2 x)}{3} + \frac{9}{3}$

Step 1.4.3.1.1.2

Cancel the common factors.

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Step 1.4.3.1.1.2.1

Factor $3$ out of $3$ .

$y = \frac{3 (2 x)}{3 (1)} + \frac{9}{3}$

Step 1.4.3.1.1.2.2

Cancel the common factor.

$y = \frac{3 (2 x)}{3 \cdot 1} + \frac{9}{3}$

Step 1.4.3.1.1.2.3

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{9}{3}$

Step 1.4.3.1.1.2.4

Divide $2 x$ by $1$ .

$y = 2 x + \frac{9}{3}$

Step 1.4.3.1.2

Divide $9$ by $3$ .

$y = 2 x + 3$

Step 2

Using the slope-intercept form, the slope is $2$ .

$m = 2$

Step 3

The equation of a perpendicular line to $y = 2 x + 3$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{2}$

Step 4