Question

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 = ?

Answer 1

Answer:

The linear relationship is;

$y=-\frac{1}{2}n+43$

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;

$\begin{gathered} 27-28=32m-30m+b-b \\ -1=2m \\ m=-\frac{1}{2} \end{gathered}$

We can then substitute to get b;

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

Therefore, the linear relationship is;

$y=-\frac{1}{2}n+43$