Calculus Examples

$6 x - y + 9 = 0$

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 $6 x$ from both sides of the equation.

$- y + 9 = - 6 x$

Step 2.2.2

Subtract $9$ from both sides of the equation.

$- y = - 6 x - 9$

Step 2.3

Divide each term in $- y = - 6 x - 9$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- y = - 6 x - 9$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 6 x}{- 1} + \frac{- 9}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 6 x}{- 1} + \frac{- 9}{- 1}$

Step 2.3.2.2

Divide $y$ by $1$ .

$y = \frac{- 6 x}{- 1} + \frac{- 9}{- 1}$

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 one from the denominator of $\frac{- 6 x}{- 1}$ .

$y = - 1 \cdot (- 6 x) + \frac{- 9}{- 1}$

Step 2.3.3.1.2

Rewrite $- 1 \cdot (- 6 x)$ as $- (- 6 x)$ .

$y = - (- 6 x) + \frac{- 9}{- 1}$

Step 2.3.3.1.3

Multiply $- 6$ by $- 1$ .

$y = 6 x + \frac{- 9}{- 1}$

Step 2.3.3.1.4

Divide $- 9$ by $- 1$ .

$y = 6 x + 9$

Step 3

Using the slope-intercept form, the slope is $6$ .

$m = 6$

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 $6$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = 6 \cdot (x - (0))$

Step 6

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

$y + 0 = 6 \cdot (x + 0)$

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

$y = 6 \cdot (x + 0)$

Step 7.2

Add $x$ and $0$ .

$y = 6 x$

Step 8