Question 848316
The line you are looking for will have the same slope as 9x-2y-5=0, because the two lines are specified to be parallel.  This means two things:


(*)  The slopes are 9/2, for both lines;
(*)  The line you want to find as standard form can be expressed as 9x-2y+c=0.


You want to solve for c, and substitute the coordinates for the point which is specified to be on the line.
{{{c=-9x+2y}}}
{{{c=-9*(-8)+2(7)}}}
{{{c=72+14}}}
{{{c=86}}}
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The line you want in your standard form is {{{highlight_green(9x-2y+86=0)}}}.


GENERAL FORM
Solve for y and adjust according to {{{highlight_green(y=mx+b)}}} format.  This is also called slope-intercept form.


POINT-SLOPE FORM
This form comes from the definition of slope.  Fitting the values into the equation, {{{highlight(y-7=(9/2)(x+8))}}}.