Question

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

Answer 1

Answer:

$P(w)=0.2w+1$

Step-by-step explanation:

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

$P(w)=mw+b$,

where $m$ is the slope of the linear equation, and $b$ is the y-intercept.

We find $m$ by evaluating the rise/ run of the linear equation:

$m= \frac{ \Delta rise}{ \Delta run} = \frac{ \Delta price}{ \Delta weight} =\frac{5-3}{20-10} =\frac{2}{10} \\\\\boxed{m=0.2}$

thus we have

$P(w)+0.2w+b$

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

$5=0.2(20)+b\\5=4+b\\\\\boxed{b=1}$

So  finally we have the function

$\boxed{P(w)+0.2w+1}$

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