There are 2 leaves along 3 in. of ivy vine. There are 14 leaves along 15 in. of the same vine. How many leaves are there along 6 in. of vine?
One less than the number of inches. (Five, in this case)
Are we supposed to assume the relation is linear, i.e., the number of leaves is directly proportional to the length of the vine??
If so, then let the length of the vine be x
let the number of leaves by y
we have two ordered pairs given (3,2) and (15,14)
slope = (14-2)/(15-3) =
then y = x + b
using (3,2)
2 = 3 + b
b = -1
then y = x - 1 , where x ≥ 1
so when x = 6, y = 5
there would be 5 leaves for a 6 inch long vine.
(common sense would have shown that the number of leaves appears to be one less than the length of vine number)
There are 2 leaves along 3 in. of an ivy vine. There are 14 leaves along 15 in. of the same vine. Which equation models the number of leaves y along x in. of vine
jkjk
A 3-mi cab ride costs $3.00. A 6-mi cab ride costs $4.80. Find a linear equation that models cost c as a function of distance d.
To solve this problem, we can set up a proportion based on the relationship between the number of leaves and the length of the vine.
Let's define the number of leaves as L and the length of the vine as V.
From the given information, we have two data points:
1) 2 leaves along 3 inches of vine
2) 14 leaves along 15 inches of vine
We can set up the proportion as follows:
2 leaves / 3 inches = 14 leaves / 15 inches
Now, let's use this proportion to find the number of leaves along 6 inches of vine.
2 leaves / 3 inches = L leaves / 6 inches
To find L, we can use cross-multiplication:
2 leaves * 6 inches = 3 inches * L leaves
12 leaves = 3 inches * L leaves
Divide both sides of the equation by 3 inches to solve for L:
12 leaves / 3 inches = L leaves
4 leaves = L leaves
Therefore, there are 4 leaves along 6 inches of vine.