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a farmer finds there is a linear relationship between the number of Beanstalk n she plants in the yield y each plant produces when the plants 30 stocks each plant yields 28 oz of beans when she plants 32 stalk each plant produces 27 oz of beans find a linear relationship in the form y =mn+ b that gives the year when n stock are planted y = ?

User Kris Erickson
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1 Answer

23 votes
23 votes

Answer:

The linear relationship is;


y=-(1)/(2)n+43

Step-by-step explanation:

A linear relationship between y and n is of the form;


y=mn+b

Where;

m = slope

b = intercept

Given;

when the plants 30 stocks each plant yields 28 oz of beans;


28=30m+b\text{ ------1}

when she plants 32 stalk each plant produces 27 oz of beans;


27=32m+b\text{ --------2}

To solve the system of equation;

Subtract equation 1 from 2;


\begin{gathered} 27-28=32m-30m+b-b \\ -1=2m \\ m=-(1)/(2) \end{gathered}

We can then substitute to get b;


\begin{gathered} 28=30m+b \\ 28=30(-(1)/(2))+b \\ 28=-15+b \\ b=28+15 \\ b=43 \end{gathered}

Therefore, the linear relationship is;


y=-(1)/(2)n+43

User Abaza
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