#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#