Question

A farmer finds there is a linear relationship between the number of bean stalks, nn, she plants and the yield, yy, each plant produces. When she plants 3030 stalks, each plant yields 3434 oz of beans. When she plants 3333 stalks, each plant produces 3333 oz of beans. Find a linear relationship in the form y

Answer 1

The linear relationship in the form y =  y = 3n + 72

What is  linear relationship?

In statistics, a straight line of correlation between two variables is referred to as a linear relationship (or linear association). The mathematical equation y = mx + b can be used to represent linear relationships graphically.

According to the given information :

Each plant generates 34 oz of beans when she plants 30 stalks, and 33 stalks results in 33 oz of beans per plant, according to the information we have provided.

Equation 1 using data 1:

                                    y = mn + b

Equation 1 using data 1:

                                    30 = 34m + b

Equation 2 using data 2:

                                     33 = 33m + b

Subtract equation 1 from equation 2:

                               33 - 30 = 34m + b - 33m - b

                                     3 = m

                                      m = 3

Rearrange equation 1 to solve for b:

                                    b = 34(3) - 30

                                      b = 102 - 30

                                      b = 72

Therefore the equation becomes:

                                     y = 3n + 72

The linear relationship in the form y =  y = 3n + 72

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