Question

The table below relates the number of rats in a population to time in weeks. Use the table to write a linear equation with w as the input variable.

P(w)=

Answer 1

`P(w)=6w+9`

Explanation:

To find the linear equation, first we need to calculate the slope of that line, we is defined as

`m=(y_(2)-y_(1) )/(x_(2) -x_(1) )`

Where we need to use two points from the table: (0,9) and (4,33).

Replacing these points, we have

`m=(33-9)/(4-0)=(24)/(4) =6`

Now, we use the point-slope formula to find the equation

`y-y_(1) =m(x-x_(1) )\\y-9=6(x-0)\\y=6x+9`

Let's call
`y=P(w)` and
`x=w`.

The equation that models the given table is

`P(w)=6w+9`

Answer 2

C(w) = 6w + 9

Explanation:

Anytime 0 is given somewhere, it should be given close scrutiny. In an equation whose general form is

y = mx + b

0 will determine the y intercept immediately.

So when x = 0, y will equal

y = 0*m + 9

So b = 9

y = mx + 9 Now we need to find m

I should start using your variables.

C(w) = m*w + 9

when w = 3 then C(3) = 27

27= 3m +9

27-9 =3m + 9 -9

18 = 3m

18/3 = 3m/3

x = 6

So the complete equation is

C(w) = 6w + 9