Pre-Algebra Examples

$17 x + 2 y = 0$

Choose a point that the perpendicular line will pass through.

$(0, 0)$

Solve $y = - \frac{17 x}{2}$ .

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Subtract $17 x$ from both sides of the equation.

$2 y = - 17 x$

Divide each term by $2$ and simplify.

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Divide each term in $2 y = - 17 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 17 x}{2}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{2 y}{2} = \frac{- 17 x}{2}$

Divide $y$ by $1$ .

$y = \frac{- 17 x}{2}$

Move the negative in front of the fraction.

$y = - \frac{17 x}{2}$

Use the slope-intercept form to find the slope.

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The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Using the slope-intercept form, the slope is $- \frac{17}{2}$ .

$m = - \frac{17}{2}$

The equation of a perpendicular line to $y = - \frac{17 x}{2}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{17}{2}}$

Simplify $- \frac{1}{- \frac{17}{2}}$ to find the slope of the perpendicular line.

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Reduce the expression by cancelling the common factors.

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

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{17}{2}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{17}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{2}{17})$

Multiply $\frac{2}{17}$ by $1$ .

$m_{perpendicular} = \frac{2}{17}$

Multiply $- - \frac{2}{17}$ .

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Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{2}{17})$

Multiply $\frac{2}{17}$ by $1$ .

$m_{perpendicular} = \frac{2}{17}$

Find the equation of the perpendicular line using the point-slope formula.

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Using the point-slope form $y - y_{1} = m (x - x_{1})$ , plug in $m = \frac{2}{17}$ , $x_{1} = 0$ , and $y_{1} = 0$ .

$y - (0) = (\frac{2}{17}) (x - (0))$

Solve for $y$ .

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Subtract $0$ from $y$ .

$y = (\frac{2}{17}) (x - (0))$

Simplify $(\frac{2}{17}) (x - (0))$ .

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Subtract $0$ from $x$ .

$y = \frac{2}{17} x$

Combine $\frac{2}{17}$ and $x$ .

$y = \frac{2 x}{17}$

Reorder terms.

$y = \frac{2}{17} x$

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