Question

Patrice and her family went to the movies. The data table below represents the amount of money they spend in dollars, f(x), in terms of the number of tickets, x,

they buy.
PART A
Write a linear function, f(x), that represents the data
PART B
Explain what the slope and y-intercept of f(x) mean in the given context.

Answer 1

f(x) = 7.75x + 12.5

The slope represents the cost per movie ticket.

The intercept represents the flat fee paid to see movies.

Explanation:

From the data given :

When x = 3 ; f(x) = 35.75

When x = 5 ; f(x) = 51. 25

Linear function :

y = mx + c

f(x) = mx + c

m = slope ; c = intercept

35.75 = 3m + c - - - (1)

51.25 = 5m + c - - - (2)

Subtract

-15.5 = - 2m

m = 15.5 / 2

m = 7.75

From (1)

35.75 = 3m + c

35.75 = 3(7.75) + c

35.75 = 23.25 + c

c = 35.75 - 23.25

c = 12.5

y = 7.75x + 12.5

f(x) = 7.75x + 12.5

B.) The slope represents the cost per movie ticket.

The intercept represents the flat fee paid to see movies.