Arecipe calls for 1/2 cup ingredient a for every 1 2/3 cups of ingredient b. you use 4 cups of ingredient a. how many cups of ingredient b do you need?

Step-by-step explanation:

A recipe calls for 1/2 cup ingredient a for every 1 2/3 cups of ingredient b.

Let us assume ingredient of b needed is b.

We have

Cups of ingredient b needed  

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: