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 32 oz of beans. When she plants 36 stalks, each plant produces 30 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.

Answer 1

y = (-1/3)n + 42

Explanation:

We can use the point-slope form of a linear equation to find the slope of the line:

slope = (y2 - y1) / (x2 - x1) = (30 - 32) / (36 - 30) = -1/3

Now we can use one of the points (30, 32) to find the y-intercept:

y = mx + b

32 = (-1/3)(30) + b

b = 42

So the linear relationship between the number of bean stalks and the yield is:

y = (-1/3)n + 42