Precalculus Examples

$2 x + 4 y + 5 = 0$

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.1

Subtract $2 x$ from both sides of the equation.

$4 y + 5 = - 2 x$

Step 2.2.2

Subtract $5$ from both sides of the equation.

$4 y = - 2 x - 5$

Step 2.3

Divide each term in $4 y = - 2 x - 5$ by $4$ and simplify.

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Step 2.3.1

Divide each term in $4 y = - 2 x - 5$ by $4$ .

$\frac{4 y}{4} = \frac{- 2 x}{4} + \frac{- 5}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 2 x}{4} + \frac{- 5}{4}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 2 x}{4} + \frac{- 5}{4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

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

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Step 2.3.3.1.1.1

Factor $2$ out of $- 2 x$ .

$y = \frac{2 (- x)}{4} + \frac{- 5}{4}$

Step 2.3.3.1.1.2

Cancel the common factors.

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Step 2.3.3.1.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 (- x)}{2 (2)} + \frac{- 5}{4}$

Step 2.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (- x)}{2 \cdot 2} + \frac{- 5}{4}$

Step 2.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{- x}{2} + \frac{- 5}{4}$

Step 2.3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{- 5}{4}$

Step 2.3.3.1.3

Move the negative in front of the fraction.

$y = - \frac{x}{2} - \frac{5}{4}$

Step 2.4

Write in $y = m x + b$ form.

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Step 2.4.1

Reorder terms.

$y = - (\frac{1}{2} x) - \frac{5}{4}$

Step 2.4.2

Remove parentheses.

$y = - \frac{1}{2} x - \frac{5}{4}$

Step 3

Using the slope-intercept form, the slope is $- \frac{1}{2}$ .

$m = - \frac{1}{2}$

Step 4

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 5

Use the slope $- \frac{1}{2}$ and a given point $(0, 0)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{2} \cdot (x - (0))$

Step 6

Simplify the equation and keep it in point-slope form.

$y + 0 = - \frac{1}{2} \cdot (x + 0)$

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

$y = - \frac{1}{2} \cdot (x + 0)$

Step 7.2

Simplify $- \frac{1}{2} \cdot (x + 0)$ .

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Step 7.2.1

Add $x$ and $0$ .

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

Step 7.2.2

Combine $x$ and $\frac{1}{2}$ .

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

Step 7.3

Write in $y = m x + b$ form.

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Step 7.3.1

Reorder terms.

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

Step 7.3.2

Remove parentheses.

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

Step 8