2x+5y -3 = 0 solve for y and look for the resulting coefficient of the x term

5y =-2x +3

y = -2x/5 +3/5 has slope =-2/5

2x-3y = 15 solve for y

-3y = -2x + 15 when solved for y, the constant term is the y intercept

y = 2x/3 - 5 has a y intercept of -5

y= -2x/5 -5 is the line parallel to the given line and with y intercept = the other given line