An international food festival charges for admission and for each sample
of food. admission and 3 samples cost $5.75. admission and 6 samples
cost $8.75.

which linear function represents the cost, y, for any number of
samples, x?

Total Cost  :   y = 2.75 +  m (1) , where m = cost of each item

Step-by-step explanation:

The cost of admission and 3 samples = $5.75

The cost of  admission and 6 samples  = $8.75.

Cost is represented by y ,

The number of Samples = x

Let the admission charge is each case = $ a.

⇒ Total Cost  y = a + (Number of items tasted x Cost of each item)

So, according to the question:

First Case:

a +  3x =  $ 5.75

Second  Case:

a +  6x =  $ 8.75

Solving the above system of equations, we get a = $ 2.75

And , if a = $2.75  then    x = 1

Hence, the Total Cost y = 2.75 +  m (1) , here m = cost of each item