Algebra Examples

$- 3 x - 7 y = 8$

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

Add $3 x$ to both sides of the equation.

$- 7 y = 8 + 3 x$

Step 1.3

Divide each term in $- 7 y = 8 + 3 x$ by $- 7$ and simplify.

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Step 1.3.1

Divide each term in $- 7 y = 8 + 3 x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{8}{- 7} + \frac{3 x}{- 7}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 7$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{8}{- 7} + \frac{3 x}{- 7}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{- 7} + \frac{3 x}{- 7}$

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

Move the negative in front of the fraction.

$y = - \frac{8}{7} + \frac{3 x}{- 7}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{8}{7} - \frac{3 x}{7}$

Step 1.4

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

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Step 1.4.1

Reorder $- \frac{8}{7}$ and $- \frac{3 x}{7}$ .

$y = - \frac{3 x}{7} - \frac{8}{7}$

Step 1.4.2

Reorder terms.

$y = - (\frac{3}{7} x) - \frac{8}{7}$

Step 1.4.3

Remove parentheses.

$y = - \frac{3}{7} x - \frac{8}{7}$

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{7}$ .

$m = - \frac{3}{7}$

Step 3

The equation of a perpendicular line to $y = - \frac{3}{7} x - \frac{8}{7}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{3}{7}}$

Step 4

Simplify the result.

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Step 4.1

Cancel the common factor of $1$ and $- 1$ .

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Step 4.1.1

Rewrite $1$ as $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{3}{7}}$

Step 4.1.2

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{3}{7}}$

Step 4.2

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{7}{3})$

Step 4.3

Multiply $\frac{7}{3}$ by $1$ .

$m_{perpendicular} = \frac{7}{3}$

Step 4.4

Multiply $- - \frac{7}{3}$ .

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Step 4.4.1

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{7}{3})$

Step 4.4.2

Multiply $\frac{7}{3}$ by $1$ .

$m_{perpendicular} = \frac{7}{3}$

Step 5