Question

A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When she plants 3 stalks, each plant yields 130 ounces of beans. When she plants 6 stalks, each plant yields 190 ounces of beans.

Select the correct answer
Y(n)=24n+58
Y(n)=24n+46
Y(n)=20n+70
Y(n)=22n+58
Y(n)=22n+64
Y(n)=20n+75

Answer 1

Answer: ok

Explanation:

Given the linear relationship between the number of bean stalks, n, and the yield, Y, we can represent this relationship using a linear equation in the form of Y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the two given points (3, 130) and (6, 190) and apply the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (190 - 130) / (6 - 3)

m = 60/3

m = 20

So the slope is 20.

To find the y-intercept, we can use the point-slope form of the linear equation and substitute one of the given points and the slope:

Y - 130 = 20(n - 3)

Simplifying this equation, we get:

Y = 20n + 70

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

Y = 20n + 70

This equation can be used to predict the yield for any number of bean stalks that the farmer may plant.