Answer:
[tex]\text{The equation which models the y number of leaves along x inches of vine : }y = \frac{4}{3}\cdot x[/tex]
Step-by-step 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
[tex]k=\frac{4}{3}[/tex]
Also, There are 20 leaves along 15 inches of an ivy vine
⇒ y = 20 , x = 15
Putting these values in (1)
⇒ 20 = k·15
[tex]k=\frac{20}{15}=\frac{4}{3}[/tex]
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.
[tex]\text{Hence, the equation which models the y number of leaves along x inches of vine : }y = \frac{4}{3}\cdot x[/tex]
