# How do you find a standard form equation for the line with A(5, 6) and is perpendicular to the line 4x+3y=8?

May 18, 2018

Therefore standard form of the perpendicular line thru A (5,6) is

color(green)(3x - 4y = -9

#### Explanation:

$4 x + 3 y = 8$

$3 y = - 4 x + 8$

$y = \left(- \frac{4}{3}\right) x + 8$, in slope - intercept form.

Slope ${m}_{1} = - \frac{4}{3}$

Slope of perpendicular line ${m}_{2} = - \frac{1}{m} _ 1 = \frac{3}{4}$

Equation of perpendicular line passing thru A(5,6) is given by

$\left(y - {y}_{A}\right) = {m}_{2} \cdot \left(x - {x}_{A}\right)$

$\left(y - 6\right) = \left(\frac{3}{4}\right) \cdot \left(x - 5\right)$

$\left(4 y - 24\right) = \left(3 x - 15\right)$

Standard form of a linear equation is given by

$a x + b y = c$

Therefore standard form of the perpendicular line thru A (5,6) is

color(green)(3x - 4y = -9