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Which equation represents a direct linear variation?
A.y = x2
B. y=1/x
C.y = x + 2
D.y = ½x

Question

anonymous · Answer

I think its B. but I might be wrong.

anonymous · Answer

@Isaiah.Feynman

da_scienceman · Answer

check which of the equations is/are not raised to any power? since x is th eindependent variable, I will check this in the RHS!

da_scienceman · Answer

For example. I  can see that C and D only relate to the dependent variable, y with nothing raised to any power!

da_scienceman · Answer

of as I see... D will be eliminated if x is in d denominator? then only C is linear in x? please check!

anonymous · Answer

@whpalmer4 what do you think it is I think its b. :)

whpalmer4 · Answer

Direct linear variation is like $y = kx$

anonymous · Answer

SO then its a.?

whpalmer4 · Answer

linear means that if you double $x$, you also double $y$, no matter what value you start with.  That would not be true of answer B.

da_scienceman · Answer

No it cant be since x is not linear in B. Check and convince yourself that a linear relationship is only observed if both x and y vary in a linear fashion! In B, u can see that x is in a reciprocal relationship with y!

whpalmer4 · Answer

A. is $y = x^2$, right?

anonymous · Answer

yes

whpalmer4 · Answer

Yeah, so if you double $x$, $y$ is quadrupled because you are squaring that factor of 2

whpalmer4 · Answer

x = 1, y = 1*1 = 1
double x to 2
x = 2, y =  2*2 = 4
oops, y went from 1 to 4 when x went from 1 to 2.  That isn't linear.

anonymous · Answer

ok so its NOT A.

whpalmer4 · Answer

We've already ruled out B.  C is intriguing, because it doesn't raise $x$ to a power:
$$y = x+2$$
x = 1, y = 1+2 = 3
x = 2, y = 2 + 2 = 4

oops, failed the linear test again — we doubled x and y did not double in response

whpalmer4 · Answer

C IS linear, but it isn't direct linear variation because of that "+2" in there.

anonymous · Answer

So then its D.

anonymous · Answer

We ruled everything else out. :)

whpalmer4 · Answer

D: $y = \frac{1}{2}x$

x = 1, y = 1/2
x = 2, y = 1
hey, we doubled x and it doubled y!  success!

anonymous · Answer

Thanks! Can I tag you in another question please?

whpalmer4 · Answer

now, a word of warning: testing two points like that isn't enough to prove that it is linear, only to prove that it isn't.  but in this case, we could use that to rule out all the other answers

anonymous · Answer

ok thanks for the pointer! :)

whpalmer4 · Answer

unfortunately I have to run...

anonymous · Answer

Awww! What will I ever do without you? haha its ok until next time! Bye!

whpalmer4 · Answer

go ahead and post it in a new post, tag me via "@whpalmer4" and I'll answer it next time I'm on, if someone else hasn't beaten me to it

anonymous · Answer

ok thanks for everything!