Question

A friend gave Ms. Morris a gift card for aa number of car washes, xlocal car wash. The table shows the linear relationship of how the value left on the amount left on card ($), y

card relates to the number of car washes.
a. Write an equation that shows the number of dollars left on the card.
b. Explain the meaning of the negative slope in this situation.
c. What is the maximum value of x that makes sense in this context? Explain.

Answer 1

The equation that shows the number of dollars left on the card is y = mx + b. The negative slope means that as the number of car washes increases, the value left on the card decreases. The maximum value of x depends on the initial value of the gift card and the cost of each car wash.

Step-by-step explanation:

a. The equation that shows the number of dollars left on the card is y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the equation would be y = (-x) + c, where c is the initial value of the gift card.

b. The negative slope in this situation means that as the number of car washes increases, the value left on the card decreases. This indicates that each car wash reduces the value on the card.

c. The maximum value of x that makes sense in this context would depend on the initial value of the gift card and how much each car wash costs. If the minimum cost of a car wash is zero, then x can take any non-negative value. However, if there is a minimum cost per car wash, then x would be limited by the maximum number of car washes that can be purchased with the initial value of the card.