(4,5);y=3/2x+3 write an equation of the line that passes through the given point that is parallel to the given line

2x-3/y-5/37=0

Step-by-step 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.

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step-by-step explanation: