Question

Please help!!!!!!!!

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:

Given:

The relation between the number of tickets and total cost for purchasing them.

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

Now, let the relation be given by the following function:

`y=mx+b`, where,
`m` and
`b` are constants.

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

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

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

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

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

Subtract equation 1 from equation 2. This gives,

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

Now, plug in
`m=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 function to represent the relationship between the tickets and total cost is given as:

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