Question

Please help!!!!!!!! this is worth 60 points!!!!!!

The table shows the relationship between the number of


tickets and the total cost to purchase tickets.


Write a function to represent the relationship.



Tickets______Price


7__________$12.25


10_________$16.00


12_________$18.50


18_________$26.00

Answer 1

`y=1.25x+3.5`

Explanation:

Let
`y` represent number of tickets and
`x` represent the total cost to purchase them.

Now,assuming the relation to be of the form:

`y=ax+b`, where,
`a` and
`b` are constants.

Let us find
`a` and
`b` using the values from the table.

For,
`x=7,y=12.25`. So,

`12.25=7a+b\\or\ 7a+b=12.25------------1`

For,
`x=10,y=16`. So,

`16=10a+b\\or\ 10a+b=16------------2`

Subtract equation 1 from equation 2. This gives,

`10a+b-7a-b=16-12.25\\(10a-7a)+(b-b)=3.75\\3a=3.75\\a=(3.75)/(3)=1.25`

Now, plug in
`a=1.25` in equation 1 and solve for
`b`

`7(1.25)+b=12.25\\8.75+b=12.25\\b=12.25-8.75=3.5`

Therefore, the relation between the number of tickets and total cost of purchase is given as:

`y=ax+b\\y=1.25x+3.5`