Question

Please help Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
x y
7 11
8 13
9 15
10 17

Answer 1

y does vary directly with x. as x increases by 1, y increases by 2.

Answer 2

thus you know that the equation is going to be something like y = 2x + @

Answer 3

plug it in anywhere, and you get y = 2x - 3

Answer 4

the constant of variation is going to be 2.

Answer 5

I don't understand what you mean

Answer 6

look at first two lines.

Answer 7

x increased from 7 to 8, right?

Answer 8

and y increased from 11 to 13.

Answer 9

yea I see that

Answer 10

ok, lets keep that in mind and keep on going from second line to third line

Answer 11

from second line to third line, x increased from 8 to 9.

Answer 12

while y increased from 13 to 15.

Answer 13

yes

Answer 14

so, from first line to second line. while x increased by 1, y increased by 2.

Answer 15

from second line to third line, while x increased by 1, y increased by 2.

Answer 16

this property is constantly shown in different lines.

Answer 17

i see that

Answer 18

"varying directly" means that the x and y changes in a constant ratio.

Answer 19

in this question, x and y changes in 1:2 ratio. while x changes 1, y changes 2.

Answer 20

if it's not varying directly, then the x and y will not have same ratio throughout the whole table. at one point, x will increase by 1 and y will increase by 2, when on the other point, x will increase by 1 and y might increase by 5

Answer 21

okay I understand so far

Answer 22

ok, first, we know that this "function" is varying directly.

Answer 23

now the second part of the question asks us what the constant of variation is.

Answer 24

thats what I dont understand

Answer 25

ok. the constant of variation only works for functions that directly vary

Answer 26

as i mentioned earlier, functions that directly vary will have a constant ratio of change between X and Y

Answer 27

basically what you have to do is find how much Y is changing as X increase by 1.

Answer 28

in this case, Y is increasing by 2 (constantly) as X increase by 1

Answer 29

thus the constant of variation is 2.

Answer 30

so do you add themtogether to get 3

Answer 31

nonono. you don't add them. you have the answer already.

Answer 32

constant of variation is "how much Y changes as X increases by 1"

Answer 33

y=2x-3 where did the -3 come from

Answer 34

ok. that's the last step.

Answer 35

functions that directly change are always in one form.

Answer 36

Y = K*X + B

Answer 37

K is the constant of variation. in this case, it's 2

Answer 38

Y and X are variables obviously, so we leave them as they are.

Answer 39

so we have Y = 2X + B

Answer 40

we have to figure out the B now.

Answer 41

thats when we go back to the table and plug in numbers for X and Y

Answer 42

im lost on this step just pug in any number

Answer 43

yes.

Answer 44

plug in any set of number (x,y) from the table

Answer 45

as in, plug in any LINE. first line, second line, whatever.

Answer 46

if you did your question correctly, then you should have the same answer for B for any line.

Answer 47

lets plug in first line. it says that X = 7 and Y = 11

Answer 48

we have Y = 2X + B

Answer 49

we plug in 11 for Y and 7 for X

Answer 50

11 = 7*2 + B

Answer 51

11 = 14 + B

Answer 52

thus we get B = -3

Answer 53

lets try plugging in second line.

Answer 54

we have X = 8 and Y = 13

Answer 55

13 = 2*8 + B

Answer 56

13=8*2+b b=13

Answer 57

13 = 16 + B.

Answer 58

uhhh.. so we have B = -3..

Answer 59

not sure how you got b = 13 from that equation.

Answer 60

thats what i got just didnt type it in right

Answer 61

yeah i thought so.

Answer 62

when you plug in the number and figure it you should get y right

Answer 63

uhm. X and Y are "variables"

Answer 64

meaning being, there aren't answers for them.

Answer 65

i mean when you like say 13=16+b if you put-3 in the equation you end up with 13

Answer 66

i think i got it thanks so much for taking tim to explain each step

Answer 67

no problem.