Precalculus Examples

$(- x) - 7 y = - 4$

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

Simplify the left side.

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Step 2.2.1

Remove parentheses.

$- x - 7 y = - 4$

Step 2.3

Add $x$ to both sides of the equation.

$- 7 y = - 4 + x$

Step 2.4

Divide each term in $- 7 y = - 4 + x$ by $- 7$ and simplify.

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Step 2.4.1

Divide each term in $- 7 y = - 4 + x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 4}{- 7} + \frac{x}{- 7}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 7$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 4}{- 7} + \frac{x}{- 7}$

Step 2.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4}{- 7} + \frac{x}{- 7}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Simplify each term.

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Step 2.4.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{4}{7} + \frac{x}{- 7}$

Step 2.4.3.1.2

Move the negative in front of the fraction.

$y = \frac{4}{7} - \frac{x}{7}$

Step 2.5

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

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Step 2.5.1

Reorder $\frac{4}{7}$ and $- \frac{x}{7}$ .

$y = - \frac{x}{7} + \frac{4}{7}$

Step 2.5.2

Reorder terms.

$y = - (\frac{1}{7} x) + \frac{4}{7}$

Step 2.5.3

Remove parentheses.

$y = - \frac{1}{7} x + \frac{4}{7}$

Step 3

Using the slope-intercept form, the slope is $- \frac{1}{7}$ .

$m = - \frac{1}{7}$

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 $- \frac{1}{7}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{7} \cdot (x - (0))$

Step 6

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

$y + 0 = - \frac{1}{7} \cdot (x + 0)$

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

$y = - \frac{1}{7} \cdot (x + 0)$

Step 7.2

Simplify $- \frac{1}{7} \cdot (x + 0)$ .

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Step 7.2.1

Add $x$ and $0$ .

$y = - \frac{1}{7} \cdot x$

Step 7.2.2

Combine $x$ and $\frac{1}{7}$ .

$y = - \frac{x}{7}$

Step 7.3

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

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Step 7.3.1

Reorder terms.

$y = - (\frac{1}{7} x)$

Step 7.3.2

Remove parentheses.

$y = - \frac{1}{7} x$

Step 8