Question

There are 4 leaves along 3 in. of an ivy vine. There are 20 leaves along 15 in. of the same vine. Which equation models the y number of leaves along x in. of vine?

Answer 1

4/3 = 1 1/3 leaves per inch of vine.

y = 1 1/3x

Hope this helps!

Answer 2

`\text{The equation which models the y number of leaves along x inches of vine : }y = (4)/(3)\cdot x`

Explanation:

Let number of leaves be x and the inches of vine along the leaves be y

Now, let the equation which models the y number of leaves along x inches of vine be : y = k·x ......(1)

As given , 4 leaves along 3 inches of an ivy vine

⇒ y = 4 , x = 3

Putting these values in (1)

⇒ 4 = k·3

`k=(4)/(3)`

Also, There are 20 leaves along 15 inches of an ivy vine

⇒ y = 20 , x = 15

Putting these values in (1)

⇒ 20 = k·15

`k=(20)/(15)=(4)/(3)`

So, k in both the cases is same hence it can be used to model the general equation for number of leaves y along x inches of vine.

`\text{Hence, the equation which models the y number of leaves along x inches of vine : }y = (4)/(3)\cdot x`