Final answer:
If r=0 in the equation a=bq+r, then a is exactly divisible by b resulting in a being the product of b and q (a=bq), which indicates a direct relationship between a and b.
Step-by-step explanation:
If r=0, then the relationship between a, b, and q in the equation a=bq+r is simply that a is directly proportional to b, meaning that a equals b times q with no remainder. The variable r represents the remainder in division, and if it is zero, then a is exactly divisible by b. This is a form of the division algorithm where a is the dividend, b is the divisor, q is the quotient, and r is the remainder.
Since r=0, the relationship can be simplified to a=bq. This means for any values of b and q, their product will yield a, signifying a direct relationship between these variables without any remainder.