Question

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 she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationships in the form y mn b   that gives the yield when n stalks are planted.

Answer 1

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

$\frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}$

Substitute the points as x =n

$\frac{y-30}{28-30} =\frac{x-30}{34-30}\\y-30 = -0.5(x-30)\\y = -0.5x+45$

is the linear relationship between n and y