You can put this solution on YOUR website! y=kx-3 is perpendicular to the line 2y+3x=7
2y=-3x+7
y=-3x/2+7/2
y=-1.5x+3.5 this line has a slope=(-1.5).
Therefore all perpendicular line will have a slope equal to the
negative inverse of this slope [-3/2 : 2/3].
Ans. y=2x/3-3