An international food festival charges for admission and for each sample of food. admission and 6 samples cost $8.25. admission and 8 samples cost $10.25. write a linear function rule to model the cost y for any number of samples x

y = x + 2.25

Step-by-step explanation:

First information: admission and 6 samples cost $8.25:

8.25 = 6a + b

Second information: admission and 8 samples cost $10.25:

10.25 = 8a + b

{6a + b = 8.25

{8a + b = 10.25

{- 6a - b = - 8.25

{8a + b = 10.25

2a = 2

a = 1

6a + b = 8.25

6.1 + b = 8.25

b = 8.25 - 6

b = 2.25

The linear function rule is:

y = x + 2.25

I hope I've helped you.

i need the options

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.