Find the Perpendicular Line through: (2,-5) , perp. to y=2/5x-1

through: $(2, - 5)$ , perp. to $y = \frac{2}{5} x - 1$

Find the slope when $y = \frac{2}{5} x - 1$ .

Rewrite in slope-intercept form.

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

$y = m x + b$

Simplify the right side.

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

$y = \frac{2 x}{5} - 1$

Reorder terms.

$y = \frac{2}{5} x - 1$

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.

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.

Use the slope $- \frac{5}{2}$ and a given point $(2, - 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

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

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

Solve for $y$ .

Simplify $- \frac{5}{2} \cdot (x - 2)$ .

Rewrite.

$y + 5 = 0 + 0 - \frac{5}{2} \cdot (x - 2)$

Simplify terms.

Apply the distributive property.

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

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

$y + 5 = - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot (2 (- 1))$

Cancel the common factor.

$y + 5 = - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot (2 \cdot - 1)$

Rewrite the expression.

$y + 5 = - \frac{x \cdot 5}{2} - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

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

Move $5$ to the left of $x$ .

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

Move all terms not containing $y$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

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

Combine the opposite terms in $- \frac{5 x}{2} + 5 - 5$ .

Subtract $5$ from $5$ .

$y = - \frac{5 x}{2} + 0$

Add $- \frac{5 x}{2}$ and $0$ .

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

Reorder terms.

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

Remove parentheses.

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

Find the Perpendicular Line through: (2,-5) , perp. to y=2/5x-1

Related Questions

Support LCMGCF.com by disabling your adblocker.