Algebra Examples

$9 x = 2 y - 1$

Choose a point that the perpendicular line will pass through.

$(0, 0)$

Solve $y = \frac{9 x}{2} + \frac{1}{2}$ .

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Rewrite the equation as $2 y - 1 = 9 x$ .

$2 y - 1 = 9 x$

Add $1$ to both sides of the equation.

$2 y = 9 x + 1$

Divide each term by $2$ and simplify.

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Divide each term in $2 y = 9 x + 1$ by $2$ .

$\frac{2 y}{2} = \frac{9 x}{2} + \frac{1}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 y}{2} = \frac{9 x}{2} + \frac{1}{2}$

Divide $y$ by $1$ .

$y = \frac{9 x}{2} + \frac{1}{2}$

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 $\frac{9}{2}$ .

$m = \frac{9}{2}$

The equation of a perpendicular line to $y = \frac{9 x}{2} + \frac{1}{2}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{9}{2}}$

Simplify $- \frac{1}{\frac{9}{2}}$ to find the slope of the perpendicular line.

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Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{2}{9}))$

Multiply $\frac{2}{9}$ by $1$ .

$m_{perpendicular} = - \frac{2}{9}$

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 $m = - \frac{2}{9}$ , $x_{1} = 0$ , and $y_{1} = 0$ .

$y - (0) = (- \frac{2}{9}) (x - (0))$

Solve for $y$ .

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Subtract $0$ from $y$ .

$y = (- \frac{2}{9}) (x - (0))$

Simplify $(- \frac{2}{9}) (x - (0))$ .

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Subtract $0$ from $x$ .

$y = - \frac{2}{9} x$

Combine $x$ and $\frac{2}{9}$ .

$y = - \frac{x \cdot 2}{9}$

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

$y = - \frac{2 x}{9}$

Reorder terms.

$y = - (\frac{2}{9} x)$

Remove parentheses.

$y = - \frac{2}{9} x$

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