The table shows the amount of seaweed powder, s, and the amount of fish powder, f, a factory uses to make different quantities of fertilizer.
Amount of
Seaweed Powder, s
(in pounds) Amount of
Fish Powder, f
(in pounds)
21.5 8.6
35.5 14.2
68.5 27.4
81.5 32.6
129.5 51.8
Which equation represents the proportional relationship between the amount of seaweed powder and the amount of fish powder in the fertilizer?
A.
B.
C.
D.
To determine the equation representing the proportional relationship between the amount of seaweed powder and the amount of fish powder in the fertilizer, we need to find the constant of proportionality (k). We can do this by selecting any two points from the table and setting up an equation of the form f = ks, where f represents the amount of fish powder and s represents the amount of seaweed powder. Let's choose the points (21.5, 8.6) and (35.5, 14.2).
Using the first set of points, we have:
8.6 = k * 21.5
Simplifying the equation, we get:
k = 8.6 / 21.5
k ≈ 0.4
Now, we can substitute the value of k into the equation f = ks to get the equation representing the proportional relationship.
The equation is:
f = 0.4s
Therefore, the correct answer is A.