Solution for Problem 2.5.1

Find the constant of proportionality.
y is directly proportional to x.  If x = 12, then y = 4.

Solve

Step

Check

The goal is to find k, the constant.

y = kx Use the formula for direct variation 

If x = 12, then y = 4.  

If x = 12, then y = 4.   Given

4 = k(12) Plug in x and y
4 = 12k Divide by 12

y = 4

constant of proportionality
Plug 1/3 in formula for k

Done
Now we have a formula that can be used to find values for y for specific values of x.