Algebra Examples

$y = - \frac{2}{5} x + \frac{4}{5}$

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 $\frac{2}{5}$ .

$y = - \frac{x \cdot 2}{5} + \frac{4}{5}$

Step 1.2.1.2

Move $2$ to the left of $x$ .

$y = - \frac{2 x}{5} + \frac{4}{5}$

Step 1.3

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

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Step 1.3.1

Reorder terms.

$y = - (\frac{2}{5} x) + \frac{4}{5}$

Step 1.3.2

Remove parentheses.

$y = - \frac{2}{5} x + \frac{4}{5}$

Step 2

Using the slope-intercept form, the slope is $- \frac{2}{5}$ .

$m = - \frac{2}{5}$

Step 3

The equation of a perpendicular line to $y = - \frac{2}{5} x + \frac{4}{5}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{2}{5}}$

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 $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{2}{5}}$

Step 4.1.2

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{2}{5}}$

Step 4.2

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{5}{2})$

Step 4.3

Multiply $\frac{5}{2}$ by $1$ .

$m_{perpendicular} = \frac{5}{2}$

Step 4.4

Multiply $- - \frac{5}{2}$ .

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Step 4.4.1

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{5}{2})$

Step 4.4.2

Multiply $\frac{5}{2}$ by $1$ .

$m_{perpendicular} = \frac{5}{2}$

Step 5