Answer:
Step-by-step explanation:
Given that a farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces
When we consider this graph as a straight line, the two points lying on the line would be
(30, 30) and (34, 28) taking n as horizontal and y vertical
Using two point equation we find that
the equation of the line is
[tex]\frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}[/tex]
Substitute the points as x =n
[tex]\frac{y-30}{28-30} =\frac{x-30}{34-30}\\y-30 = -0.5(x-30)\\y = -0.5x+45[/tex]
is the linear relationship between n and y
The linear relationship is [tex]y = -0.5n + 45[/tex]
From the question, we have the following parameters:
(n,y) = (30,30) and (34,28)
The linear equation is then calculated as:
[tex]y = \frac{y_2 -y_1}{n_2 -n_1}(n - n_1) + y_1[/tex]
Substitute known values in the above equation
[tex]y = \frac{28 -30}{34 -30}(n - 30) + 30[/tex]
Evaluate the quotient
[tex]y = -0.5(n - 30) + 30[/tex]
Open the bracket
[tex]y = -0.5n + 15 + 30[/tex]
Evaluate the sum
[tex]y = -0.5n + 45[/tex]
Hence, the linear relationship is [tex]y = -0.5n + 45[/tex]
Read more about linear equations at:
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