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Math Help - Need help with a review question

  1. #1
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    Need help with a review question

    Write the line parallel to the line with the equation x-5y=6 and through point (10,2) in standard form.

    If anyone can explain this to me, i would greatly appreciate it.
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  2. #2
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    Standard form for a line is Ax+By=c where \frac{-A}{B} is the slope of the line. So in order for the line you want to be parallel to x-5y=6, it needs to have the same slope. Solving this equation by subracting x from both sides and then dividing by -5 we get x-5y-x=6-x=-5y=6-x so \frac{-5y}{-5}=\frac{6-x}{-5} so y=\frac{6}{-5}+\frac{x}{5} so the slope is \frac{1}{5}

    So our line needs to be y=mx+b and we now know m=\frac{1}{5}

    now we need it to go through the point (10,2), so we can plug that point into the equation to solve for b. 10 is x and 2 is y so 2=\frac{1}{5}(10)+b and solving for b, b=2-2=0

    So y=\frac{1}{5}x which is parallel to the given line and contains the point (10,2)

    To get it in standard form simply subtract \frac{1}{5}x from both sides to get \frac{-1}{5}x+y=0
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