Question 1045941
2y=3x-1
finding the Slope
the standard slope-intercept form for an equation of a line is {{{y = highlight_green(m)x + highlight(b)}}}  
where m is the slope and b the y-intercept.  
2y=3x-1
Solving for y
y =-(3/2)x +1/2  Green Line
m = -3/2
Slope of Line perpendicular is 2/3 (negative reciprocal)
***Using point-slope form, {{{y - y[1] = highlight_green(m)(x - x[1])}}}
y +3 = (2/3)( x - 1)   Pt (1,-3) on this perpendicular line
y = (2/3)x -2/3  -  9/3
y = (2/3)x - 11/3 Blue Line
{{{drawing(300,300,   -6, 6, -6, 6, grid(1), 


circle(1,-3, 0.3),
circle(0,.5, 0.3),
circle(0,-11/3, 0.3),
graph( 300, 300, -6, 6, -6, 6,0, -(3/2)x +1/2,(2/3)x - 11/3 ) )}}}