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Answer 1 · 2017-02-27T10:57:25

$"the equation of the line is -2 x+3 y=13 or "y=2/3 x+13/3$

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$color(blue)(2y+3x-4=0)" the equation of the blue line"$

$"let's rearrange the equation of the blue line"$

$color(blue)(2y=-3x+4)$

$color(blue)(y=-3/2 x+2) " (1)"$

$y=m x+n " represents the standard form of the line"$

$"where m is slope of line"$

$m=-3/2$

$"let the slope of the red line perpendicular to the blue line be " m_1$

$m*m1=-1$

$-3/2*m_1=-1$

$m_1=2/3$

$"now we can use the slope-intercept form of the equation of line"$
$color(red)(y-y_1=m(x-x_1)$

$color(red)(y-3=2/3(x+2))$

$color(red)(y-3=2/3 x+4/3)$

$color(red)(y=2/3 x+4/3+3)$

$color(red)(y=2/3 x+13/3)$

$"or "$

$"let's multiply both sides of equation by 3"$

$3y=2x+13$

$-2x+3y=13$