Question

X and y have a proportional relationship, and y = 6 when x = 3. Which equation represents this?

Answer 1

x = 1/2y .

Explanation:

Here it is given that ,

• x and y have a proportional relationship. Since it's not mentioned whether it is direct or indirect I am assuming it to be direct .

We can write this mathematically as,

`\longrightarrow x \propto y`

If we assume k to be constant , then ,

`\longrightarrow x = ky \ ..... (i)`

Again when y = 6 , the value of x is 3 , so that;

`\longrightarrow 3 = k(6)`

Divide both sides by 6 ,

`\longrightarrow (3)/(6)=k`

Simplify ,

`\longrightarrow k =(1)/(2)`

Now substitute the value of k in equation (i),

`\longrightarrow\underline{\underline{ x =(1)/(2)y}}`

This is the required answer!

Answer 2

Here, x and y have a proportional relationship.So, we can write this as –

x ∝ y

↠ x = cy (c = constant). . . Eq(1)

Now, we are given x =3 and y = 6. We have to find out the value of c so just substitute the values of x and y into Eq(1).

↠ 3 = c × 6

↠ c = 3/6

↠ c = 1/2

• Therefore, value of c is 1/2.

Substituting value of c in Eq(1)–

↠ x = 1/2 y

or, y = 2x.