Question

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASE!!!!!!!!!!!!!!!!!!
Is the relationship between each pair of values is a direct variation or an inverse variation? And explain:)

A. (2, 10), (7,35), (12,60)
B. (0.8, 4), (1.6, 2), (5, .64)
C. (1.5, 4), (2,3), (12, 0.5)

Answer 1

I'll solve the first for you, then you try
a) (2, 10), (7, 35), (12, 60)
as the first term increases the second term also increases
2-> 7-> 12
10->35->60
In fact if you multiply first by 5, you'll get the second term
Do you get this? @kaykim95

Answer 2

Yes i get it

Answer 3

Now check b and c, find if they are direct or indirect variation

Answer 4

*inverse

Answer 5

and what are inverse and direct variation for those equations? Like what would the first one be?

Answer 6

Second term= first * 5

Answer 7

so 5x, would it be inverse or direct??? I don't understand that

Answer 8

it's direct, as first term increases second also increases

Answer 9

could u define inverse and direct?

Answer 10

Let's have a relation
\[b=\frac 1 a\]
This is the simplest inverse relation
a=1 b=1
a=2 b=0.5
a=4 b=0.25
You can see the behavior of b is opposite to a, can't you?

Answer 11

@kaykim95 ???

Answer 12

so that equation is inverse?

Answer 13

and yes i see it

Answer 14

Yes, if I have something like
\[b=2a\]
This is an example of direct relation

Answer 15

a=1 b=2
a=2 b=4
a=3 b=6 and so on...
Similar behavior of a and b

Answer 16

so, for direct variation use b=2a, and for inverse use b= 1/a, if you have points to the function?

Answer 17

No these were just an example, standard relation are
Direct:
\[y=ax\]
Inverse:
\[y=\frac a x\]
y=second term
x=first term
You would need to find a, it can vary
for part a of our question a=5

Answer 18

* for part A of our question a=5

Answer 19

Do you get it @kaykim95 ?
I gotta bounce, I'll be back in 15 minutes

Answer 20

so is A. a=5?

Answer 21

What are the answers for B and C?

Answer 22

B and C are inverse relation
so the equation which they will follow is
\[y=\frac a x\]
Take any of the points say (0.8, 4)
\[4=\frac a {0.8}\]
Can you find a from this?

Answer 23

are they inverse because they are decreasing substantially from each one? or increasing?

and a is 3.2

Answer 24

Yeah, they are inverse as the second term decreases substantially as first increases

Answer 25

You are right
Now do the same steps for C part

Answer 26

@kaykim95 Are you trying?

Answer 27

Direction variation-The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways.

Inverse variation-The phrase “ y varies inversely as x” or “ y is inversely proportional to x” means that as x gets bigger, y gets smaller, or vice versa. This concept is translated in two ways.

Answer 28

Example a) you see the x values increasing constantly as well as the y values.
x by 5 and y by 25
therefore it is a direct variation.

Example b) you see the x values and y values do not increase or decrease constantly so it has to be an inverse variation.

Follow @ash2326's working above and ask me if you don't get it.

Example c) apply the same concept from example b.