Answer:
2x-3/y-5/37=0
Explanation:
here, given equation of line is
y=3/2x+3
or,y(2x+3)=3
or,2x+3=3/y
or,2x-3/y+3=0...eqn(i)
equation of any line parallel to line (i) is
2x-3/y+k=0.. eqn(ii)
since, the line passes through (4,5)[replacing x=4 and y=5 in eqn(ii), we get]
2*4-3/5+k=0
or,8-3/5+k=0
or,40-3/5+k=0
or,k=-5/37
substituting the value of k=-5/37 in eqn(ii)
2x-3/y-5/37=0 is the required equation of line.