Question 1066457: Find the equation of the line through (-6,10), parallel to the line with equation 3x-7y=14. Write the new equation in point-slope form. Convert the equation of the new line to standard form, Ax+By=C, where A, B, and C are integers.
Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 3x-7y=14
-7y=-3x+14
y=(3x/7)-2
the slope is (3/7)
Parallel lines have the same slope
point slope formula y-y1=m(x-x1), where m is the slope (3/7) and (x1,y1) the point.
y-10=(3/7)(x+6)
y-10=(3x/7)+(18/7)
y=(3/7)x+(88/7)
multiply by 7
move x to left
multiply by -1 to make coefficient of x positive
7y=3x+88
3x-7y=-88
Answer by josgarithmetic(39616)  (Show Source):
You can put this solution on YOUR website! -----------------------------------------------------------------
...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.
 , the right side member is simply the left-expression with the included point substituted.
Simplifying,  ,
 ---------the standard form for the equation asked for.
Note, the slope is still unchanged, because also "parallel" line was wanted.
The slope is still  . To put the desired equation into point-slope form, containing point (-6,10),  .
Putting into point-slope form first, and then converting into standard form Ax+By=C was not necessary.
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