The table shows the total cost, p, for renting a playroom for a birthday party with c party guests. Number of Party Guests (C) Total Cost (p), in Dollars 3 274 7 306 12 346 21 418 Which of the following equations represents the input/output table using function notation? O A. p = 8c + 250 O B. p = 258c C. f(c) = 8c + 250 O D. f(p) = 8c - 250

Option (A)

Step-by-step explanation:

Let the equation of the linear function representing number of party guests (c) and total cost (p) is in the form of c = mp + b

m = Slope of the line

b = y-intercept

Choose the two ordered pairs from the table (3, 274) and (7, 306).

Slope of the function 'm' =

m =

m = 8

Since, equation of a line passing through (x', y') and slope m is,

y - y' = m(x - x')

Therefore, equation of a line passing through (3, 274) and slope = 8,

y - 274 = 8(x - 3)

y - 274 = 8x - 24

y = 8x + 274 - 24

y = 8x + 250

Since, y = p and x = c

Therefore, p = 8c + 250 will be the equation.

Option (A) is the answer.

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Step-by-step explanation: the answer is A

c

step-by-step explanation: