Question 1066457
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...equation of the line through (-6,10), parallel to the line with equation 3x-7y=14. 
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The entire left-side member can be kept the same to keep in STANDARD FORM.
{{{3x-7y=3(-6)-7(10)}}}, the right side member is simply the left-expression with the included point substituted.


Simplifying,  {{{-18-70=-88}}},
{{{highlight(3x-7y=-88)}}}---------the standard form for the equation asked for.


Note, the slope is still unchanged, because also "parallel" line was wanted.

The slope is still {{{3/7}}}.  To put the desired equation into point-slope form,  containing  point  (-6,10),  {{{highlight(y-10=(3/7)(x+6))}}}.


Putting into point-slope form first, and then converting into standard form Ax+By=C was not necessary.