Question

Which of the following scenarios models the equation y=2x+5?

There are initially 5 chickens on the farm. Each month thereafter the number of chickens is 2 times the number in the month before.
Nina earns $2.00 for each Enjoy the City book she sells. Each time she sells a book she also gets a five-dollar tip.
The temperature at 8:00 AM is 5 degrees Celsius and increases 2 degrees per hour.

Answer 1

Equation : y=2x+5

A) There are initially 5 chickens on the farm. Each month thereafter the number of chickens is 2 times the number in the month before.

Since Every time the the number of chickens is 2 times the number in the month before. So, it is not the case

B)Nina earns $2.00 for each Enjoy the City book she sells. Each time she sells a book she also gets a five-dollar tip.

Let x be the number of books

She earns per book = 2

She earns by selling x books = 2x

we are given that Each time she sells a book she also gets a five-dollar tip.

So, Total cost of selling x books = 2x+5

So, This scenario models the equation y=2x+5

C)The temperature at 8:00 AM is 5 degrees Celsius and increases 2 degrees per hour.

Initial temperature = 5°C

Change in temp per hour = 2°C

Change in temp in x hours = 2x

So, Temperature after x hours - 2x+5

So, This scenario models the equation y=2x+5

Answer 2

Option 3

Explanation:

Option 1:

Each month thereafter the number of chickens is 2 times the number in the month before.

This is not the case. It is easy to note because it has no mention of the 5 the function has as independent term. So discard it.

Option 2:

Nina earns $2.00 for each Enjoy the City book she sells. Each time she sells a book she also gets a five-dollar tip.

If X is the books sold, the $2 per book fits the equation, but as the $5 also varies with the books sold, this option does not fit. The 5 term must be fixed, not varying with X.

Option 3:

The temperature at 8:00 AM is 5 degrees Celsius and increases 2 degrees per hour.

This is correct!

X is the hours from 8:00. The day begins with 5dg and then increases by 2dg every hour. In te following hours there will be:

9:00 - 2+5=7

10:00 - 4+5=9

11:00 - 6+5=11

12:00 - 7+5=13

And so on!