Given the table, let's create a function rule that describes the relationship between the number of people served and the number of pots of coffee.
To create a function rule, let's first find the average rate of change.
Take two points on the table:
(x1, y1) ==> (2, 12)
(x2, y2) ==> (3, 18)
Apply the slope formula:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{18-12}{3-2} \\ \\ m=\frac{6}{1} \\ \\ m=6 \end{gathered}[/tex]
The slope or average rate of change is 6.
Aply the slope intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
In this case the function will be:
s(p) = mp + b
To find b, input the values of one point for x and y, and substitute 6 for m.
Thus, we have:
y = mx + b
Take the first point:
(x, y) ==> (2, 12)
12 = 6(2) + b
12 = 12 + b
Subtract 12 from both sides:
12 - 12 = 12 - 12 + b
0 = b
To write a function rule, we have:
s(p) = 6p + 0
s(p) = 6p
Therefore, the function rule to describe the relationship between the number of people served and the number of pots of coffee is:
[tex]s(p)=6p[/tex]
ANSWER:
[tex]s(p)=6p[/tex]
