Direct Variation Question?

Question

ok, i understand HOW to do direct variation but i am one of those people who has to know WHY the formula works. they say y=kx. i believe that. but WHY do they multiply the slope and the x coordinate?? why not add them, or divide, or multiply, hugh? PLEASE someone answer this question!! i will give you a lot of points i just need help, i am soooo confused!!!!!!

thanks for all your answers but i still dont get why you multiply the slope! please help

Bramblyspam, you made me understand it. my teacher wouldn't help me, thanks for YOU helping me :)
it wont let me choose your answer until 4 hrs. so yea.

Answer 1

OK... so you get the idea that "direct variation" is a line that goes through the origin, yes? Since it's a line, it has the same slope (or "rise over run") everywhere.

Let's look at an example. Let's say you're looking at a direct variation with a slope of 2.

A slope of 2 means that if you go 1 step in the x-direction, you have to go up 2 steps in the y-direction.

If you take a second step in the x-direction, then you have to go up an additional 2 steps in the y-direction.

If you take a third step in the x-direction, then you have to go up still 2 more steps in the y-direction.

Generalizing: To figure out the total distance you move upward in the y-direction, just take the number of steps you move in the x-direction and multiply that by two.

In other words, y = 2x, when your slope is 2.
Similarly, y = kx, when your slope is k.

Hopefully that helps!

Answer 2

The term direct just means that y is proportional to x and proportionate just means that y=kx for some number k. A more general linear equation, which is given by y=mx+b is not direct because after you multiply some number by x you still have to add the constant b in order to get your y value.

Answer 3

Think of k as the proportion of variation.

The easiest example I can think of is a short person and a tall person walking together, call the short person y and the tall person x. If y has to take 2 steps for every one step x takes, then the number of steps y takes is in direct proportion to the number of steps x takes. Without knowing exactly how many steps x has taken, you can't explicitly define what number to add to that to get the number of steps y has taken. In general you do know that y has taken twice as many steps as x though, so you get the formula y=2x to descibe this situation.

Hope that helps.

Answer 4

V immediately varies with r^3, permit V1 be first quantity it is = 8 pi R1 is the 1st radius it is = 2 if V2 is the 2d quantity it is = sixty 4 pi and R2 is the 2d radius, V1/V2 = R1^3/R2^3 8/sixty 4 = 2^3/R2^3 R2^3= 8*8 So R2 = 4

Answer 5

ok, think about it. this may sound nasty but it will explain it. when you have sex, how come you dont orgasm when you see the guy's face. because that is how the body is made, and how it works. it cannot work in any other way, and the only way to orgasm is for a certain process to happen. same in math, you can only get ther correct answer if you do something a certain way. sorry i couildnt explain it in any other way.