Precalculus Examples

$8 x + 4 y = 2$

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

Subtract $8 x$ from both sides of the equation.

$4 y = 2 - 8 x$

Step 1.3

Divide each term in $4 y = 2 - 8 x$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 y = 2 - 8 x$ by $4$ .

$\frac{4 y}{4} = \frac{2}{4} + \frac{- 8 x}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{2}{4} + \frac{- 8 x}{4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{4} + \frac{- 8 x}{4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Cancel the common factor of $2$ and $4$ .

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Step 1.3.3.1.1.1

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{4} + \frac{- 8 x}{4}$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 1}{2 \cdot 2} + \frac{- 8 x}{4}$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot 2} + \frac{- 8 x}{4}$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{1}{2} + \frac{- 8 x}{4}$

Step 1.3.3.1.2

Cancel the common factor of $- 8$ and $4$ .

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Step 1.3.3.1.2.1

Factor $4$ out of $- 8 x$ .

$y = \frac{1}{2} + \frac{4 (- 2 x)}{4}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $4$ out of $4$ .

$y = \frac{1}{2} + \frac{4 (- 2 x)}{4 (1)}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = \frac{1}{2} + \frac{4 (- 2 x)}{4 \cdot 1}$

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = \frac{1}{2} + \frac{- 2 x}{1}$

Step 1.3.3.1.2.2.4

Divide $- 2 x$ by $1$ .

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

Step 1.4

Reorder $\frac{1}{2}$ and $- 2 x$ .

$y = - 2 x + \frac{1}{2}$

Step 2

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

$m = - 2$

Step 3

The equation of a perpendicular line to $y = - 2 x + \frac{1}{2}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

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Step 4.1

Move the negative in front of the fraction.

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

Step 4.2

Multiply $- - \frac{1}{2}$ .

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Step 4.2.1

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{1}{2})$

Step 4.2.2

Multiply $\frac{1}{2}$ by $1$ .

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

Step 5