Algebra Examples

$y = 3 x + 6$

Choose a point that the perpendicular line will pass through.

$(0, 0)$

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 $3$ .

$m = 3$

The equation of a perpendicular line to $y = 3 x + 6$ must have a slope that is the negative reciprocal of the original slope.

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

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 $m = - \frac{1}{3}$ , $x_{1} = 0$ , and $y_{1} = 0$ .

$y - (0) = (- \frac{1}{3}) (x - (0))$

Solve for $y$ .

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Subtract $0$ from $y$ .

$y = (- \frac{1}{3}) (x - (0))$

Simplify $(- \frac{1}{3}) (x - (0))$ .

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Subtract $0$ from $x$ .

$y = - \frac{1}{3} x$

Combine $x$ and $\frac{1}{3}$ .

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

Reorder terms.

$y = - (\frac{1}{3} x)$

Remove parentheses.

$y = - \frac{1}{3} x$

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