Question

the table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.

automatic feeder

number of meals dispensed, n	amount of pet food remaining, f(n) (cups)
3	15
6	6
7	3

based on the table, which function models this situation?
f f(n)= - 3n + 24
g f(n)= -\frac{1}{3}n + 18
h f(n)= - 3n+84
j f(n)= -\frac{1}{3}n + 8

Explanation:

Step1: Recall slope - intercept form

The linear function is of the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,21)$ and $(x_2,y_2)=(3,15)$.
$m=\frac{15 - 21}{3 - 1}=\frac{-6}{2}=-3$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(1,21)$ and $m=-3$.
$y-21=-3(x - 1)$.
Expand: $y-21=-3x + 3$.
Add 21 to both sides: $y=-3x+24$. In the context of the problem with $n$ as the independent variable and $f(n)$ as the dependent variable, $f(n)=-3n + 24$.

Answer:

F. $f(n)=-3n + 24$