Question

Can someone please explain how to solve this problem? Thanks.

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

X Y
4 6.4
7 11.2
10 16
13 20.8

Answer 1

no y does not varie as x

Answer 2

x/y should = to x in all examples

Answer 3

how does it not vary with x, how do i check it myself

Answer 4

y varies directly with x

means

y= k x
where k is some constant number.

This is one of the simplest equations you will meet.
if you have an (x,y) pair, you can replace the x and y in the equation and solve for k:

for the first entry in your table, you have x=4 and y is 6.4
replace y with 6.4, and x with 4 in y = k x to get
6.4= k * 4
divide both sides by 4:
6.4/4 = k * 4/4
or
k= 6.4/4 = 1.6

so your direct variation equation is
y= 1.6 x

if the other pairs in your table "work" then you can say they all have the same equation, and y varies directly with x (with k= 1.6)

can you test the other (x,y) values in your table ?

Answer 5

yes, just give me a moment please

Answer 6

all x*1.6 equals the y values in the chart so y DOES directly vary with x, right?

Answer 7

yes

Answer 8

thank you so much, i think its easy now :D

Answer 9

yw

Answer 10

sorry it was my calcuation error....i did a calcualtion error for 13 and 20.8

Answer 11

i am very sorry