Question

find the value for k such that the slope of the line whose equation is given will equal 8.
(k-4)x+2y=10

Answer 1

slope of \(ax+by=c\) is \(-\frac{a}{b}\) so set
\[-\frac{k-4}{2}=8\] and solve for \(k\)

Answer 2

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

Answer 3

some mistake here

Answer 4

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

Answer 5

oh okay. but is that how i would solve for the k ?

Answer 6

the mistake you made was here
\[-\frac{k-4}{2}=8\\-k-4=16\]

Answer 7

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
\[-(k-4)=16\\-k+4=16\\-k=12\\k=-12\]

Answer 8

or you could start with
\[-\frac{k-4}{2}=8\] and change it to
\[\frac{k-4}{2}=-8\]

Answer 9

or you could even multiply both sides by \(-2\) and get
\[-\frac{k-4}{2}=8\\k-4=-16\]

Answer 10

you can check that \(-12\) is the right answer by substitution

Answer 11

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 \(x=4\)

Answer 12

so i could start the equation by plugging -12 in for k. so:
(-12-4)x+2y=10
then i could slove from there

Answer 13

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

Answer 14

okay thank you!(: