Question

suppose y varies directly with x. if y=-3 when y=5,find y when x=-1

Answer 1

i think something wrong in ur question

Answer 2

suppose y varies directly with x. if y=-3 when X*?=5,find y when x=-1

Answer 3

I think that the answer is y=3

Answer 4

x y
-1 3
0 2
1 1
2 0
3 -1
4 -2
5 -3

Answer 5

If y varies directly with x, then \(y = kx\), \(k\) some constant. \(-3 = k *5\rightarrow k=-\frac{3}{5}\)

\(y = k(-1)\)\[y = -\frac{3}{5}(-1) = \frac{3}{5}\]

@cahayes9498 with direct variation, you've just got a straight line, and the slope is \(k\). Here \(k = -\frac{3}{5}\) so the line slopes down and to the right. Your table would be correct if we knew that \(k = -1\), but it doesn't, so the relationship between x and y is not correct.

Answer 6

@whpalmer4 you have me completely lost now, where is the K coming in at?

Answer 7

Any variation problem has a scale factor in there. We have to find it using the initial data. So, because it is direct variation, we know the form is \(y = kx\). If we double \(x\), \(y\) also doubles. That's direct variation. Now, the reason the \(k\) factor is there is so we can have direct variation between any possible pair of \(x\) and \(y\) values. Say I had two quantities that exhibited direct variation, but when the \(x\) value was 1, the \(y\) value was 3. How do you make that happen, except by a scale factor? You can't just add (which is what your table did) because then doubling \(x\) won't double \(y\).

Answer 8

Looking at it another way: with this problem, we knew that y = -3 when x = 5. Well, if it is direct variation, then doubling \(x\) must also double \(y\). If we evaluate my function at x = 10, we get \(y = -\frac{3}{5}(10) = -6\) which is twice the value it is at x = 5. With your table, y would = -8, and that isn't a doubling of what it was at x = 5.

Answer 9

Does that make sense?

Answer 10

ok I understand it now, yes it makes sense now

Answer 11

Good! Are you comfortable with the difference between direct, indirect and joint variation?

Answer 12

yes

Answer 13

Also good. Each of them will have that pesky \(k\) in the numerator.

Answer 14

Have you taken any physics classes?

Answer 15

Lots of variation examples there, and although the variation constant isn't usually called \(k\), it's always there. Perhaps the most obvious one is Newton's F=ma — for a given mass, the acceleration a and force F vary directly, and m serves as the variation constant.

Answer 16

no I have not

Answer 17

Another example might be the distance formula: distance = speed * time. If you go at a steady speed, the distance varies directly with the time. Double the time, double the distance. Here the speed is the variation constant.

I think I've beaten this horse to death, or at least bored it :-)