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 (in ounces). 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 an equation that gives the yield y when n stalks are planted.

Answer 1

`y = -(1)/(2)n + 15`

Explanation:

Linear equation:

A linear equation has the following format:

`y(n) = an + b`

In which a is the slope and b is the y-intercept.

When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans.

This means that we have these following two points: (30,30) and (34,28).

Finding the slope:

When we have two points, the slope is given by the change in the output y divided by the change in the input n.

Change in the output: 30 - 28 = 2.

Change in the input: 30 - 34 = -4. So

`a = (2)/(-4) = -(1)/(2)`

So

`y = -(1)/(2)n + b`

Finding b:

When
`n = 30, y = 30`. We replace this into the equation to find b. So

`y = -(1)/(2)n + b`

`b = -(1)/(2)(30) + 30`

`b = -15 + 30 = 15`

So

`y = -(1)/(2)n + 15`