Can someone explain direct variation to me?

Question

Like which of these are direct variation and why?
y=5/2x
y=x+4
y=4
I am very confused

Answer 1

it's very simple dear..

Equation I
y=5/2x is indirect variation b'cos as the value of x increases, the value of y decreases and vice versa

let us substitue x=5, then we get
y=5/2(5)
y=1/2 ==> 0.5

let us substitute x=10, we now get
y=5/2(10) => 1/4 => 0.25

Equation II
y=x+4

this is direct variation cos as you increase the value of x, the value of y wud also increase and vice versa

let us substitute different values for x
let x be 7
y=7+4
y = 11

let x be 2
y=2+4
y=6

thus this is direct variation

Equation III
y=4... this is neither cos there is no x..

Answer 2

The third one is not really a variation because y is always the same. It is a constant. Besides, there is no other unknown involved in that relationship anyway.
In a direct variation as one unknown changes the other also proportionately changes in the same way - that is, in the same "direction". For instance , as one increases, the other increases. With the second one , as x increases (or decreases) , y also increases (or decreases) in some manner. Here the proportion or ratio of that change happens to be is 1:1. As x increases or decreases, y will also increase or decrease the same amount and y will always be 4 larger than whatever x is.
In the first example it it was written y = (5/2) x it would also be a direct relation. The ration is 5/2 :1. However, if it was written y= 5/ (2x) then it would be an inverse relation because as x increases, y decreases by that same ratio.

Answer 3

By definition, a direct variation function is where if the x value is increase by a certain factor (i.e., multiplied), the matching y value will also increase by that same factor.

For example, let's say you're driving on a highway at a speed of 60 miles per hour. Therefore, the distance you travel since the start of your trip is the amount of time you've driven multiplied by 60. The equation for this is d = 60*t.

After you've driven, say, 3 hours, your distance is 60*3 = 180 miles. If you double your time (to 6 hours), your distance also doubles (60*6 = 360, which is double of 180).

We would then say that d=60t is a direct variation. Whenever the time changes by a given multiplication factor, the distance also changes by that same multiplication factor.

In equations, a direct variation is a linear equation with zero for its y-intercept and a slope that is neither 0 (a horizontal line) nor undefined (a vertical line).

All your equations are linear. But only the first, y = 5/2 * x, has a y-intercept of 0. It's slope is 5/2 which is neither zero nor undefined. So y = 5/2 * x is your direct variation.

An example by definition as to why it is: if x=4, then y would be equal to 10. If x is increased by a factor of 3 so that x=12, then y = 30, which has also increased by a factor of 3.

Answer 4

Direct Variation: X goes up, Y goes up.
Example: Food intake and weight

Indirect Variation: X goes up, Y goes down
Example: House price and potential buyers

In your three examples, the first, y=5/2x, this is indirect variation. If X goes up, the denominator gets larger, so 5/ larger denominator = smaller Y
For y=x+4, this is direct variation. As X increases, so does Y.
The last example in neither direct nor indirect. There is no X to affect Y. This expression is a "Constant"
I hope this helps. Good luck!

Answer 5

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Answer 6

variation is similar to proportion
y = k x . . . means y varies with the y, or y is proportional to x with a certain factor k
it might be y is twice x, of y is 2.5 that of x, just like your number 1 question
y = k / x. . . means that y varies inversely with x

you second and third question is seldom used as variation expressions

Answer 7

direct variatoin means that as x increases, y increases

y = kx

if i work for 10 hours and i get 100 dollars at the end of the day, how much am i payed per hour?

100 = k(10)

k = 10

i get 10 dollars per hour.

the constant of variation, (k) = 10

Answer 8

When two variable quantities have a constant (unchanged) ratio, their relationship is called a direct variation.
It is said that one variable "varies directly" as the other.

The constant ratio is called the constant of variation.

The formula for direct variation is y = kx,
where k is the constant of variation.
"y varies directly as x"
Solving for k:
(y = numerator; x = denominator)

hey i think that should be y=4(2x) for instance.



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http://www.purplemath.com/modules/variatn.htm
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