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

Answer:

$P(w)=6w+9$

Step-by-step explanation:

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

$m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

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

Replacing these points, we have

$m=\frac{33-9}{4-0}=\frac{24}{4} =6$

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

Answer:

C(w) = 6w + 9

Step-by-step 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