# Question 7f0f6

Feb 27, 2017

$\text{the equation of the line is -2 x+3 y=13 or } y = \frac{2}{3} x + \frac{13}{3}$

#### Explanation:

$\textcolor{b l u e}{2 y + 3 x - 4 = 0} \text{ the equation of the blue line}$

$\text{let's rearrange the equation of the blue line}$

$\textcolor{b l u e}{2 y = - 3 x + 4}$

$\textcolor{b l u e}{y = - \frac{3}{2} x + 2} \text{ (1)}$

$y = m x + n \text{ represents the standard form of the line}$

$\text{where m is slope of line}$

$m = - \frac{3}{2}$

$\text{let the slope of the red line perpendicular to the blue line be } {m}_{1}$

$m \cdot m 1 = - 1$

$- \frac{3}{2} \cdot {m}_{1} = - 1$

${m}_{1} = \frac{2}{3}$

$\text{now we can use the slope-intercept form of the equation of line}$
color(red)(y-y_1=m(x-x_1)#

$\textcolor{red}{y - 3 = \frac{2}{3} \left(x + 2\right)}$

$\textcolor{red}{y - 3 = \frac{2}{3} x + \frac{4}{3}}$

$\textcolor{red}{y = \frac{2}{3} x + \frac{4}{3} + 3}$

$\textcolor{red}{y = \frac{2}{3} x + \frac{13}{3}}$

$\text{or }$

$\text{let's multiply both sides of equation by 3}$

$3 y = 2 x + 13$

$- 2 x + 3 y = 13$