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

Answer: option d.

Step-by-step 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:

$k=\frac{2}{3}$

Substitute k into the expression. Then the equation is:

 $y=\frac{2}{3}x$

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

$y=\frac{2}{3}*1=\frac{2}{3}$

Answer 2

Answer:

Final answer is choice D. $y=\frac{2}{3}$, $y(1)=\frac{2}{3}$

Step-by-step 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)

$\frac{2}{3} =k$

Hence constant of variation is $k=\frac{2}{3}$

Now plug the value of k into formula y=kx

we get required equation as  $y=\frac{2}{3}x$

Now plug the value of x=1 into above formula

$y=\frac{2}{3}x$

$y=\frac{2}{3}(1)$

$y=\frac{2}{3}$

Hence final answer is choice D. $y=\frac{2}{3}$, $y(1)=\frac{2}{3}$