Find the Perpendicular Line y=4/5x+3 ; P=(4,-4)

$y = \frac{4}{5} x + 3$ ; $P = (4, - 4)$

Find the slope when $y = \frac{4}{5} x + 3$ .

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 $\frac{4}{5}$ and $x$ .

$y = \frac{4 x}{5} + 3$

Reorder terms.

$y = \frac{4}{5} x + 3$

Using the slope-intercept form, the slope is $\frac{4}{5}$ .

$m = \frac{4}{5}$

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

$m_{perpendicular} = - \frac{1}{\frac{4}{5}}$

Simplify $- \frac{1}{\frac{4}{5}}$ to find the slope of the perpendicular line.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{5}{4}))$

Multiply $\frac{5}{4}$ by $1$ .

$m_{perpendicular} = - \frac{5}{4}$

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

Use the slope $- \frac{5}{4}$ and a given point $P = (4, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = - \frac{5}{4} \cdot (x - (4))$

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

$y + 4 = - \frac{5}{4} \cdot (x - 4)$

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

Solve for $y$ .

Simplify $- \frac{5}{4} \cdot (x - 4)$ .

Rewrite.

$y + 4 = 0 + 0 - \frac{5}{4} \cdot (x - 4)$

Simplify terms.

Apply the distributive property.

$y + 4 = - \frac{5}{4} x - \frac{5}{4} \cdot - 4$

Combine $x$ and $\frac{5}{4}$ .

$y + 4 = - \frac{x \cdot 5}{4} - \frac{5}{4} \cdot - 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$y + 4 = - \frac{x \cdot 5}{4} + \frac{- 5}{4} \cdot - 4$

Factor $4$ out of $- 4$ .

$y + 4 = - \frac{x \cdot 5}{4} + \frac{- 5}{4} \cdot (4 (- 1))$

Cancel the common factor.

$y + 4 = - \frac{x \cdot 5}{4} + \frac{- 5}{4} \cdot (4 \cdot - 1)$

Rewrite the expression.

$y + 4 = - \frac{x \cdot 5}{4} - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$y + 4 = - \frac{x \cdot 5}{4} + 5$

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

$y + 4 = - \frac{5 x}{4} + 5$

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

Subtract $4$ from both sides of the equation.

$y = - \frac{5 x}{4} + 5 - 4$

Subtract $4$ from $5$ .

$y = - \frac{5 x}{4} + 1$

Reorder terms.

$y = - (\frac{5}{4} x) + 1$

Remove parentheses.

$y = - \frac{5}{4} x + 1$

Find the Perpendicular Line y=4/5x+3 ; P=(4,-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.