Algebra Examples

$7 x + 9 y = - 1$

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

Subtract $7 x$ from both sides of the equation.

$9 y = - 1 - 7 x$

Step 2.3

Divide each term in $9 y = - 1 - 7 x$ by $9$ and simplify.

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Step 2.3.1

Divide each term in $9 y = - 1 - 7 x$ by $9$ .

$\frac{9 y}{9} = \frac{- 1}{9} + \frac{- 7 x}{9}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $9$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 1}{9} + \frac{- 7 x}{9}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 1}{9} + \frac{- 7 x}{9}$

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

Move the negative in front of the fraction.

$y = - \frac{1}{9} + \frac{- 7 x}{9}$

Step 2.3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{1}{9} - \frac{7 x}{9}$

Step 2.4

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

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Step 2.4.1

Reorder $- \frac{1}{9}$ and $- \frac{7 x}{9}$ .

$y = - \frac{7 x}{9} - \frac{1}{9}$

Step 2.4.2

Reorder terms.

$y = - (\frac{7}{9} x) - \frac{1}{9}$

Step 2.4.3

Remove parentheses.

$y = - \frac{7}{9} x - \frac{1}{9}$

Step 3

Using the slope-intercept form, the slope is $- \frac{7}{9}$ .

$m = - \frac{7}{9}$

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 $- \frac{7}{9}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{7}{9} \cdot (x - (0))$

Step 6

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

$y + 0 = - \frac{7}{9} \cdot (x + 0)$

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

$y = - \frac{7}{9} \cdot (x + 0)$

Step 7.2

Simplify $- \frac{7}{9} \cdot (x + 0)$ .

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Step 7.2.1

Add $x$ and $0$ .

$y = - \frac{7}{9} \cdot x$

Step 7.2.2

Combine $x$ and $\frac{7}{9}$ .

$y = - \frac{x \cdot 7}{9}$

Step 7.2.3

Move $7$ to the left of $x$ .

$y = - \frac{7 x}{9}$

Step 7.3

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

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Step 7.3.1

Reorder terms.

$y = - (\frac{7}{9} x)$

Step 7.3.2

Remove parentheses.

$y = - \frac{7}{9} x$

Step 8