#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#