Question

Help and hurry pls Bc it needs to be turned in

Answer 1

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:

`\begin{gathered} m=(y2-y1)/(x2-x1) \\ \\ m=(18-12)/(3-2) \\ \\ m=(6)/(1) \\ \\ m=6 \end{gathered}`

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:

`s(p)=6p`

ANSWER:

`s(p)=6p`