Final answer:
The balance on Marvin's gift card as a linear function of the number of car washes he gets is given by the formula b = B - Cn. This represents a linear equation with B as the starting balance, C as the cost per car wash, and n as the number of car washes.
Step-by-step explanation:
To create a formula for the balance on Marvin's gift card as a linear function of the number of car washes he gets, we need two pieces of information: the starting balance on the gift card, and the cost of one car wash. Assume the starting balance is represented by B, and the cost per car wash is represented by C. Then, if n represents the number of car washes, the balance b after purchasing the car washes would be B minus the total cost of the car washes (which is C times n).
The formula for the balance b on the gift card after n car washes would then be:
b = B - Cn
This is a linear equation because it can be represented graphically as a straight line, where b decreases at a constant rate as n increases. The slope of this line would be -C (since each car wash reduces the balance by the cost C), and the y-intercept would be the initial balance B.