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A 10- ounce box of cereal cost $3. A 20-ounce box of the same cereal cost $5. A third box of the same cereal cost $8. • Use the given relationships to write a linear equation that expresses the price of a box of cereal as a function of the number of ounces of cereal in the box. Show your work !!!
Help me out , only have 5 minutes !!! Asap ! Will give brainliest too

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Poltergeist

Answer:

[tex]P(w)=0.2w+1[/tex]

Step-by-step explanation:

Let is call [tex]P[/tex] the price of the cereal box, and [tex]w[/tex] its weight, then the linear  equation of the price [tex]P(w)[/tex] as a function of weight [tex]w[/tex] will be

[tex]P(w)=mw+b[/tex],

where [tex]m[/tex] is the slope of the linear equation, and [tex]b[/tex] is the y-intercept.

We find [tex]m[/tex] by evaluating the rise/ run of the linear equation:

[tex]m= \frac{ \Delta rise}{ \Delta run} = \frac{ \Delta price}{ \Delta weight} =\frac{5-3}{20-10} =\frac{2}{10} \\\\\boxed{m=0.2}[/tex]

thus we have

[tex]P(w)+0.2w+b[/tex]

now we figure out [tex]b[/tex] from the point ($5, 20 ounces):

[tex]5=0.2(20)+b\\5=4+b\\\\\boxed{b=1}[/tex]

So  finally we have the function

[tex]\boxed{P(w)+0.2w+1}[/tex]

which expresses the price of a box of cereal as a function of the number of ounces of cereal in the box

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