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 28 oz of beans. When she
plants 34 stalks, each plant produces 26 oz of beans. Find a linear relationship in the form
y = mn + b that gives the yield when n stalks are planted.

Answer 1

The linear relationship between the number of bean stalks planted (n) and the yield (y) each plant produces is y = -0.5n + 43, based on the provided data points and the calculation of the slope and y-intercept.

Step-by-step explanation:

To find a linear relationship in the form y = mn + b that gives the yield, y, when n stalks are planted, we can use the two given points: (30, 28) and (34, 26).

The slope, m, of the line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two given points.

Thus, the slope m is (26 - 28) / (34 - 30)

= -2 / 4

= -0.5.

To find the y-intercept, b, we can substitute one of the points into the equation y = mx + b.

For example, using the point (30, 28): 28 = (-0.5)*30 + b.

Solving for b, we get b = 28 + 15

= 43.

Therefore, the linear relationship is y = -0.5n + 43.