Finite Math Examples

$(6, 9)$ , $x + 6 y = 7$

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

Subtract $x$ from both sides of the equation.

$6 y = 7 - x$

Step 1.3

Divide each term in $6 y = 7 - x$ by $6$ and simplify.

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Step 1.3.1

Divide each term in $6 y = 7 - x$ by $6$ .

$\frac{6 y}{6} = \frac{7}{6} + \frac{- x}{6}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $6$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{7}{6} + \frac{- x}{6}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{6} + \frac{- x}{6}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$y = \frac{7}{6} - \frac{x}{6}$

Step 1.4

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

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Step 1.4.1

Reorder $\frac{7}{6}$ and $- \frac{x}{6}$ .

$y = - \frac{x}{6} + \frac{7}{6}$

Step 1.4.2

Reorder terms.

$y = - (\frac{1}{6} x) + \frac{7}{6}$

Step 1.4.3

Remove parentheses.

$y = - \frac{1}{6} x + \frac{7}{6}$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{6}$ .

$m = - \frac{1}{6}$

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

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

Step 5

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

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

Step 6

Solve for $y$ .

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Step 6.1

Simplify $- \frac{1}{6} \cdot (x - 6)$ .

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Step 6.1.1

Rewrite.

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

Step 6.1.2

Simplify by adding zeros.

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

Step 6.1.3

Apply the distributive property.

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

Step 6.1.4

Combine $x$ and $\frac{1}{6}$ .

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

Step 6.1.5

Cancel the common factor of $6$ .

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Step 6.1.5.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

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

Step 6.1.5.2

Factor $6$ out of $- 6$ .

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

Step 6.1.5.3

Cancel the common factor.

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

Step 6.1.5.4

Rewrite the expression.

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

Step 6.1.6

Multiply $- 1$ by $- 1$ .

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

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 $9$ to both sides of the equation.

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

Step 6.2.2

Add $1$ and $9$ .

$y = - \frac{x}{6} + 10$

Step 6.3

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

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Step 6.3.1

Reorder terms.

$y = - (\frac{1}{6} x) + 10$

Step 6.3.2

Remove parentheses.

$y = - \frac{1}{6} x + 10$

Step 7