Finite Math Examples

$y = - \frac{5}{6} x + 3$ , $(6, - 1)$

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

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 $\frac{5}{6}$ .

$y = - \frac{x \cdot 5}{6} + 3$

Step 1.2.1.2

Move $5$ to the left of $x$ .

$y = - \frac{5 x}{6} + 3$

Step 1.3

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

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Step 1.3.1

Reorder terms.

$y = - (\frac{5}{6} x) + 3$

Step 1.3.2

Remove parentheses.

$y = - \frac{5}{6} x + 3$

Step 2

Using the slope-intercept form, the slope is $- \frac{5}{6}$ .

$m = - \frac{5}{6}$

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 $- \frac{5}{6}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 1) = - \frac{5}{6} \cdot (x - (6))$

Step 5

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

$y + 1 = - \frac{5}{6} \cdot (x - 6)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $- \frac{5}{6} \cdot (x - 6)$ .

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Step 6.1.1

Rewrite.

$y + 1 = 0 + 0 - \frac{5}{6} \cdot (x - 6)$

Step 6.1.2

Simplify terms.

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Step 6.1.2.1

Apply the distributive property.

$y + 1 = - \frac{5}{6} x - \frac{5}{6} \cdot - 6$

Step 6.1.2.2

Combine $x$ and $\frac{5}{6}$ .

$y + 1 = - \frac{x \cdot 5}{6} - \frac{5}{6} \cdot - 6$

Step 6.1.2.3

Cancel the common factor of $6$ .

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Step 6.1.2.3.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$y + 1 = - \frac{x \cdot 5}{6} + \frac{- 5}{6} \cdot - 6$

Step 6.1.2.3.2

Factor $6$ out of $- 6$ .

$y + 1 = - \frac{x \cdot 5}{6} + \frac{- 5}{6} \cdot (6 (- 1))$

Step 6.1.2.3.3

Cancel the common factor.

$y + 1 = - \frac{x \cdot 5}{6} + \frac{- 5}{6} \cdot (6 \cdot - 1)$

Step 6.1.2.3.4

Rewrite the expression.

$y + 1 = - \frac{x \cdot 5}{6} - 5 \cdot - 1$

Step 6.1.2.4

Multiply $- 5$ by $- 1$ .

$y + 1 = - \frac{x \cdot 5}{6} + 5$

Step 6.1.3

Move $5$ to the left of $x$ .

$y + 1 = - \frac{5 x}{6} + 5$

Step 6.2

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

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Step 6.2.1

Subtract $1$ from both sides of the equation.

$y = - \frac{5 x}{6} + 5 - 1$

Step 6.2.2

Subtract $1$ from $5$ .

$y = - \frac{5 x}{6} + 4$

Step 6.3

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

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Step 6.3.1

Reorder terms.

$y = - (\frac{5}{6} x) + 4$

Step 6.3.2

Remove parentheses.

$y = - \frac{5}{6} x + 4$

Step 7