Write a equation in slope intercept form for the line that passes through (0,2) and is parallel to the line whose equation is 3x=5y+3

slope-intercept form: Y-Y₁=m(X-X₁) where m= slope

First find m: since the unknown equation is parallel to 3x=5y+3, set the later equation to y= form to find the slope ->

3x-3=5y+3-3

(3x-3)/5=5y/5

y= 3/5x-3/5

so m=3/5

 

Then plug in the coordinates (0,2) into the slope-intercept form and use your m, and you're done :D

Y-2= 3/5(x-0)

and you can simplify that into a y= form:

y=3/5x+2