Find the Perpendicular Line through: (1,-5) , perp. to y=1/8x+2

through: $(1, - 5)$ , perp. to $y = \frac{1}{8} x + 2$

Find the slope when $y = \frac{1}{8} x + 2$ .

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 $\frac{1}{8}$ and $x$ .

$y = \frac{x}{8} + 2$

Reorder terms.

$y = \frac{1}{8} x + 2$

Using the slope-intercept form, the slope is $\frac{1}{8}$ .

$m = \frac{1}{8}$

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

$m_{perpendicular} = - \frac{1}{\frac{1}{8}}$

Simplify $- \frac{1}{\frac{1}{8}}$ to find the slope of the perpendicular line.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 8)$

Multiply $8$ by $1$ .

$m_{perpendicular} = - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$m_{perpendicular} = - 8$

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

Use the slope $- 8$ and a given point $(1, - 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 5) = - 8 \cdot (x - (1))$

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

$y + 5 = - 8 \cdot (x - 1)$

Solve for $y$ .

Simplify $- 8 \cdot (x - 1)$ .

Rewrite.

$y + 5 = 0 + 0 - 8 \cdot (x - 1)$

Simplify by adding zeros.

$y + 5 = - 8 \cdot (x - 1)$

Apply the distributive property.

$y + 5 = - 8 x - 8 \cdot - 1$

Multiply $- 8$ by $- 1$ .

$y + 5 = - 8 x + 8$

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

Subtract $5$ from both sides of the equation.

$y = - 8 x + 8 - 5$

Subtract $5$ from $8$ .

$y = - 8 x + 3$

Find the Perpendicular Line through: (1,-5) , perp. to y=1/8x+2

Related Questions

Support LCMGCF.com by disabling your adblocker.