How do you write an equation of a line passing through (6, 1), perpendicular to 4y - 2 = 3x?

Oct 2, 2017

$3 y + 4 x = 27$

Explanation:

$4 y - 2 = 3 x$
$4 y = 3 x + 2$
$y = \left(\frac{3}{4}\right) x + \left(\frac{1}{2}\right)$
Slope of the line $m 1 = \frac{3}{4}$
Slope of perpendicular line $m 2 = - \frac{1}{m 1} = - \left(\frac{1}{\frac{3}{4}}\right) = - \left(\frac{4}{3}\right)$
Equation of the perpendicular line
$\left(y - 1\right) = - \left(\frac{4}{3}\right) \left(x - 6\right)$
$3 y - 3 = - 4 x + 24$
$3 y + 4 x = 27$