Question

can someone help me?
for the data in the table, does y vary directly with x? if it does, write an equation for the direct variation

X Y
8 11
16 22
24 33

Answer 1

The first part of this question asks, does x vary with y...so answer that first, how does x change with each change in y?

Answer 2

3
6
8
? I don't know im confused

Answer 3

You're close, check the math on that last one and I think you'll see that it's not 8.

Answer 4

ok is it 9?

Answer 5

Yes, now if you were to set it up as a table like this, can you see the pattern?
If X=8, then y=x+3
if X=16, then y=x+6
if X=24, then y=x+9

Answer 6

yes I see the pattern

Answer 7

Good, so how could you turn that into an equation?

Answer 8

I don't know y=mx+3
I don't know im still kind of confused

Answer 9

That's a good first guess. But look and see that 'x' never changes, you in fact increment the number (n) added to 'x'.
So what if you wrote it out like this instead:
If X=8, then y=x+(1*3)
if X=16, then y=x+(2*3)
if X=24, then y=x+(3*3)

Answer 10

So what changes, what variable could you use to count up from your 0?

Answer 11

im sorry but im still not understanding

Answer 12

Okay, so you know that you have 'x', and whatever 'x' is equal to, you add to it to get 'y'.

Answer 13

You also can see that you are counting up by 1 each time and multiplying that by 3, and then adding it to 'x'.

Answer 14

You are counting, 1, 2, 3, 4, .... , all the way to 'n'. So could you write it like this?
y = x + 3n, where n is equal to (1, 2, 3, 4, ... n)

Answer 15

oh I didn't know that's what you were asking yeah I understand that now

Answer 16

Yeah, you were very close, I knew you could get it.

Answer 17

thank you:) but are we done with the problem them?

Answer 18

Yes, you found the way that 'y' varied with 'x', and you have created an equation to describe that behavior, y = x + 3n, n=1,2,3,...n

Answer 19

oh ok now I really understand thank you for your time

Answer 20

You're quite welcome. :)
Good luck.