If b is directly proportional to a and b=2 when a=1, express b in terms of a.

Step 1: Understand the problem The problem states that b is directly proportional to a. This means that as a increases, b increases at the same rate, and vice versa. We are also given that b=2 when a=1.

Step 2: Write the proportionality equation In mathematics, direct proportionality is expressed as b = ka, where k is the constant of proportionality.

Step 3: Substitute the given values into the equation We know that b=2 when a=1. So, we substitute these values into the equation to find the value of k. 2 = k*1

Step 4: Solve for k From the equation in step 3, we find that k = 2.

Step 5: Write the final equation Now that we know the value of k, we can write the final equation that expresses b in terms of a. So, b = 2a.