Finite Math Examples

$y = - \frac{8}{3} x - 8$ , $(8, 5)$

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

Simplify the right side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Combine $x$ and $\frac{8}{3}$ .

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

Step 1.2.1.2

Move $8$ to the left of $x$ .

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

Step 1.3

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

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Step 1.3.1

Reorder terms.

$y = - (\frac{8}{3} x) - 8$

Step 1.3.2

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{8}{3}$ .

$m = - \frac{8}{3}$

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 $- \frac{8}{3}$ and a given point $(8, 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (5) = - \frac{8}{3} \cdot (x - (8))$

Step 5

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

$y - 5 = - \frac{8}{3} \cdot (x - 8)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $- \frac{8}{3} \cdot (x - 8)$ .

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Step 6.1.1

Rewrite.

$y - 5 = 0 + 0 - \frac{8}{3} \cdot (x - 8)$

Step 6.1.2

Simplify by adding zeros.

$y - 5 = - \frac{8}{3} \cdot (x - 8)$

Step 6.1.3

Apply the distributive property.

$y - 5 = - \frac{8}{3} x - \frac{8}{3} \cdot - 8$

Step 6.1.4

Combine $x$ and $\frac{8}{3}$ .

$y - 5 = - \frac{x \cdot 8}{3} - \frac{8}{3} \cdot - 8$

Step 6.1.5

Multiply $- \frac{8}{3} \cdot - 8$ .

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Step 6.1.5.1

Multiply $- 8$ by $- 1$ .

$y - 5 = - \frac{x \cdot 8}{3} + 8 (\frac{8}{3})$

Step 6.1.5.2

Combine $8$ and $\frac{8}{3}$ .

$y - 5 = - \frac{x \cdot 8}{3} + \frac{8 \cdot 8}{3}$

Step 6.1.5.3

Multiply $8$ by $8$ .

$y - 5 = - \frac{x \cdot 8}{3} + \frac{64}{3}$

Step 6.1.6

Move $8$ to the left of $x$ .

$y - 5 = - \frac{8 x}{3} + \frac{64}{3}$

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 $5$ to both sides of the equation.

$y = - \frac{8 x}{3} + \frac{64}{3} + 5$

Step 6.2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{8 x}{3} + \frac{64}{3} + 5 \cdot \frac{3}{3}$

Step 6.2.3

Combine $5$ and $\frac{3}{3}$ .

$y = - \frac{8 x}{3} + \frac{64}{3} + \frac{5 \cdot 3}{3}$

Step 6.2.4

Combine the numerators over the common denominator.

$y = - \frac{8 x}{3} + \frac{64 + 5 \cdot 3}{3}$

Step 6.2.5

Simplify the numerator.

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Step 6.2.5.1

Multiply $5$ by $3$ .

$y = - \frac{8 x}{3} + \frac{64 + 15}{3}$

Step 6.2.5.2

Add $64$ and $15$ .

$y = - \frac{8 x}{3} + \frac{79}{3}$

Step 6.3

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

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Step 6.3.1

Reorder terms.

$y = - (\frac{8}{3} x) + \frac{79}{3}$

Step 6.3.2

Remove parentheses.

$y = - \frac{8}{3} x + \frac{79}{3}$

Step 7