anonymous
  • anonymous
find the value for k such that the slope of the line whose equation is given will equal 8. (k-4)x+2y=10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
slope of \(ax+by=c\) is \(-\frac{a}{b}\) so set \[-\frac{k-4}{2}=8\] and solve for \(k\)
anonymous
  • anonymous
okay so i multiplied 2 to 8 and got -k-4=16 then i added 4 and got -k=20 but i forgot how to get rid of the negative
anonymous
  • anonymous
some mistake here

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anonymous
  • anonymous
but let me answer your question first, because you should not be confused by \[-k=20\] if \(-k=20\) then \(k=-20\) just change the sign but that is not the right answer
anonymous
  • anonymous
oh okay. but is that how i would solve for the k ?
anonymous
  • anonymous
the mistake you made was here \[-\frac{k-4}{2}=8\\-k-4=16\]
anonymous
  • anonymous
the numerator carries its own invisible parentheses that is because of the order of operations you would compute in the numerator and then divide you have a choice you could write \[-\frac{k-4}{2}=8\] then multiply by 2 and get \[-(k-4)=16\\-k+4=16\\-k=12\\k=-12\]
anonymous
  • anonymous
or you could start with \[-\frac{k-4}{2}=8\] and change it to \[\frac{k-4}{2}=-8\]
anonymous
  • anonymous
or you could even multiply both sides by \(-2\) and get \[-\frac{k-4}{2}=8\\k-4=-16\]
anonymous
  • anonymous
you can check that \(-12\) is the right answer by substitution
anonymous
  • anonymous
but solving \(-x=c\) is not hard if \(-x=c\) then \(x=-c\) for example if \(-x=5\) then \(x=-5\) and if \(-x=-4\) then \(x=4\)
anonymous
  • anonymous
so i could start the equation by plugging -12 in for k. so: (-12-4)x+2y=10 then i could slove from there
anonymous
  • anonymous
sure you would get \(-16x+2y=10\) and if you solve for \(y\) you get \[2y=16x+10\] or \[y=8x+5\] a line with slope \(8\) as required
anonymous
  • anonymous
okay thank you!(:

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