Final answer:
To find the value of b when a=5, given that a and b are proportional and a=12 corresponds to b=3, the proportionality constant k is 1/4. Thus, for a=5, b is 5/4 or 1.25.
Step-by-step explanation:
When we say that two variables, such as a and b, are proportional, we are expressing a direct proportion between them. In this case, if a = 12 corresponds to b = 3, the proportionality constant k can be found by dividing b by a, which gives us k = 3/12 = 1/4. Therefore, the relationship between a and b can be represented by the equation b = (1/4)a.
To find the value of b when a = 5, we substitute 5 for a into the equation: b = (1/4) * 5 = 5/4. Hence, when a = 5, b equals 5/4 or 1.25.