Question

nevaeh uses a gift card to buy a cup of coffee every morning. the table shows the amount of money left on the card, $y$, as a function of the number of cups of coffee she buys, $x$.
number of cups of coffee, $x$ | amount of money left on card ($), $y$
2 | 19
5 | 10
7 | 4

1. find and describe the rate of change of the function.
2. the rate of change is $\boldsymbol{?}$. it represents $\boldsymbol{?}$ in the amount on the gift card nevaeh purchases.

options for the first blank:
options for the second blank: an increase, a decrease

Explanation:

Step1: Calculate rate of change

$\text{Rate of change} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 19}{5 - 2} = \frac{-9}{3} = -3$

Step2: Interpret the rate

A negative rate means the card balance decreases as coffee is purchased.

Answer:

The rate of change is $\boldsymbol{-3}$. It represents a decrease in the amount on the gift card Nevaeh purchases.