Precalculus Examples

$9 x - 8 y - 3 = 0$ , $(- 6, 1)$

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

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

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Step 1.2.1

Subtract $9 x$ from both sides of the equation.

$- 8 y - 3 = - 9 x$

Step 1.2.2

Add $3$ to both sides of the equation.

$- 8 y = - 9 x + 3$

Step 1.3

Divide each term in $- 8 y = - 9 x + 3$ by $- 8$ and simplify.

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Step 1.3.1

Divide each term in $- 8 y = - 9 x + 3$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 9 x}{- 8} + \frac{3}{- 8}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 8$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 9 x}{- 8} + \frac{3}{- 8}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 9 x}{- 8} + \frac{3}{- 8}$

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

Dividing two negative values results in a positive value.

$y = \frac{9 x}{8} + \frac{3}{- 8}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = \frac{9 x}{8} - \frac{3}{8}$

Step 1.4

Reorder terms.

$y = \frac{9}{8} x - \frac{3}{8}$

Step 2

Using the slope-intercept form, the slope is $\frac{9}{8}$ .

$m = \frac{9}{8}$

Step 3

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

Step 4

Use the slope $\frac{9}{8}$ and a given point $(- 6, 1)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (1) = \frac{9}{8} \cdot (x - (- 6))$

Step 5

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

$y - 1 = \frac{9}{8} \cdot (x + 6)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $\frac{9}{8} \cdot (x + 6)$ .

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Step 6.1.1

Rewrite.

$y - 1 = 0 + 0 + \frac{9}{8} \cdot (x + 6)$

Step 6.1.2

Simplify by adding zeros.

$y - 1 = \frac{9}{8} \cdot (x + 6)$

Step 6.1.3

Apply the distributive property.

$y - 1 = \frac{9}{8} x + \frac{9}{8} \cdot 6$

Step 6.1.4

Combine $\frac{9}{8}$ and $x$ .

$y - 1 = \frac{9 x}{8} + \frac{9}{8} \cdot 6$

Step 6.1.5

Cancel the common factor of $2$ .

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Step 6.1.5.1

Factor $2$ out of $8$ .

$y - 1 = \frac{9 x}{8} + \frac{9}{2 (4)} \cdot 6$

Step 6.1.5.2

Factor $2$ out of $6$ .

$y - 1 = \frac{9 x}{8} + \frac{9}{2 \cdot 4} \cdot (2 \cdot 3)$

Step 6.1.5.3

Cancel the common factor.

$y - 1 = \frac{9 x}{8} + \frac{9}{2 \cdot 4} \cdot (2 \cdot 3)$

Step 6.1.5.4

Rewrite the expression.

$y - 1 = \frac{9 x}{8} + \frac{9}{4} \cdot 3$

Step 6.1.6

Combine $\frac{9}{4}$ and $3$ .

$y - 1 = \frac{9 x}{8} + \frac{9 \cdot 3}{4}$

Step 6.1.7

Multiply $9$ by $3$ .

$y - 1 = \frac{9 x}{8} + \frac{27}{4}$

Step 6.2

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

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Step 6.2.1

Add $1$ to both sides of the equation.

$y = \frac{9 x}{8} + \frac{27}{4} + 1$

Step 6.2.2

Write $1$ as a fraction with a common denominator.

$y = \frac{9 x}{8} + \frac{27}{4} + \frac{4}{4}$

Step 6.2.3

Combine the numerators over the common denominator.

$y = \frac{9 x}{8} + \frac{27 + 4}{4}$

Step 6.2.4

Add $27$ and $4$ .

$y = \frac{9 x}{8} + \frac{31}{4}$

Step 6.3

Reorder terms.

$y = \frac{9}{8} x + \frac{31}{4}$

Step 7