Question

Determine whether y varies directly with x if so find the constant of variation k write the equation

\
picture

Answer 1

direct variation is
when x increases, y increases
when x decreases, y decreses

easy

so pick any 2 values or use logic
hmm
x's, from 7 to 10 is increasing
y's from 11 to 17 is increasing
both increaseing
it's direct variation

to find it
we find slope since this probably has a b added
slope=(y2-y1)/(x2-x1)=(13-11)/(8-7)=2/1=2
k=2

Answer 2

No, y does not vary directly with x

Explanation:

Suppose y varies directly with x,

i.e. y ∝ x

⇒ y = kx,

Where, k is the constant of variation,

If x = 7, y = 11

⇒ 11 = 7k

⇒ k =
`(11)/(7)`,

Thus, the equation that shows the relation between x and y,

`y=(11)/(7)x`

If x = 8,
`y=(88)/(7)\\eq 13`

If x = 9,
`y=(99)/(7)\\eq 15`

If x = 10,
`y=(110)/(7)\\eq 17`

Hence, our assumption is wrong,

y does not vary directly with x,