Question 848251
NOTE: Edited because of mistake with slope-----Now been corrected.


The slopes are the same for parallel lines in the plane.  Keeping in the given standard form, The equation you want to find is 2x-5y+c=0.  Solve for c and then substitute the given point needed to be on the line.


{{{c=-2x+5y}}}
{{{c=-2(-9)+5*3}}}
{{{c=18+15}}}
{{{c=33}}}
The line then in standard form is {{{highlight(-2x+5y+33=0)}}}.


You wanted the equation in both point-slope form and in general form.


GENERAL FORM:
Solve for y and adjust into general form, variable term plus (or minus) constant term.  Solving for y will give a formula; not a value.


POINT-SLOPE FORM:
You will be able to read the slope directly from the "general" form or from the standard form; and then use the formula for slope (which is vertical change divided by horizontal change) to obtain the point-slope form.
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You will see that slope {{{m=2/5}}}.  Doing the steps, you will find {{{highlight(y-3=(2/5)(x+9))}}}.