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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)=

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 variablePw class=

Respuesta :

jcherry99

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

Answer:

[tex]P(w)=6w+9[/tex]

Step-by-step explanation:

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

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

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

Replacing these points, we have

[tex]m=\frac{33-9}{4-0}=\frac{24}{4} =6[/tex]

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

[tex]y-y_{1} =m(x-x_{1} )\\y-9=6(x-0)\\y=6x+9[/tex]

Let's call [tex]y=P(w)[/tex] and [tex]x=w[/tex].

The equation that models the given table is

[tex]P(w)=6w+9[/tex]

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