Find the Perpendicular Line y=2/5x (5,2)

$y = \frac{2}{5} x$ $(5, 2)$

Find the slope when $y = \frac{2}{5} x$ .

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Rewrite in slope-intercept form.

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

$y = m x + b$

Combine $\frac{2}{5}$ and $x$ .

$y = \frac{2 x}{5}$

Rewrite in slope-intercept form.

$y = \frac{2}{5} x$

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

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

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

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

Simplify $- \frac{1}{\frac{2}{5}}$ to find the slope of the perpendicular line.

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Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

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Use the slope $- \frac{5}{2}$ and a given point $(5, 2)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Simplify the equation and keep it in point-slope form.

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

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

$y = - \frac{5}{2} x + \frac{29}{2}$

Find the Perpendicular Line y=2/5x (5,2)

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