Question 174317
I can only guess at the equation of the given line because you didn't state it as an equation, however both likely possibilities result in the same equation, so I'm going to assume you meant:


{{{3x-5y=2}}}


Step 1 is to solve your equation for {{{y}}}, that is, add {{{-3x}}} to both sides, then multiply both sides by {{{-1/5}}}.  The resulting coefficient on x will be the slope of the given line.


Step 2:  Parallel lines have equal slopes, so to find the equation of a parallel line, you need to find the equation that passes through the given point ({{{x[1]}}},{{{y[1]}}}) = (4, -1) with the same slope as the given line.  We'll just call that slope {{{m}}} for this discussion, but you will replace {{{m}}} with the slope value you determined in Step 1.  Knowing the slope and a point, you can determine the equation of a line using the point-slope form of a line:


{{{y-y[1]=m(x-x[1])}}}.


Just substitute the calculated value for {{{m}}} and the given coordinates for {{{x[1]}}} and {{{y[1]}}}, and simplify.  Since your given line was presented in standard form {{{Ax+By=C}}} and the desired form for your answer is not specified, your answer should be presented in standard form as well.