Question

Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.

Answer 1

Final answer is choice D.
`y=(2)/(3)`,
`y(1)=(2)/(3)`

Explanation:

Given that if y varies directly as x, and y=2 when x=3, then we need to find out y-value when x=1.

We also need to find the constant of variation and the equation.

Since y varies directly as x so we can write equation

y=kx

where k is constant of variation.

Plug given values y=2 and x=3

2=k(3)

`(2)/(3) =k`

Hence constant of variation is
`k=(2)/(3)`

Now plug the value of k into formula y=kx

we get required equation as
`y=(2)/(3)x`

Now plug the value of x=1 into above formula

`y=(2)/(3)x`

`y=(2)/(3)(1)`

`y=(2)/(3)`

Hence final answer is choice D.
`y=(2)/(3)`,
`y(1)=(2)/(3)`

Answer 2

Answer: option d.

Explanation:

Based on the information given, you can write the following expression:

`y=kx`

Where k is the the constant of variation

If y=2 when x=3, then you can substitute these values into the expression and solve for k:

`k=(2)/(3)`

Substitute k into the expression. Then the equation is:

`y=(2)/(3)x`

Substitute x=1 into the equation. Then, y is:

`y=(2)/(3)*1=(2)/(3)`