Question

Oliver is watching a farmer plant a vegetable garden. He notices two hours after they began that the farmer had planted seven rows of the garden. Three hours later, he noticed that the farmer had now planted seventeen and a half rows of the garden. Assume that the farmer works at a constant rate.

Part B)Create an equation to represent the rate at which the farmer plants his vegetables, where x equals the hours worked and y equals the number of rows planted.

Answer 1

y = 3.5x

Explanation:

The equation for a straight line is

y = mx +b

We know that when

x₁ = 2, y₁ = 7 and when

x₂ = 5, y₂ = 17.5

Step 1. Determine the slope

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

m = (17.5 – 7)/(5 – 2) Remove parentheses

m = 10.5/3

m = 3.5

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Step 2. Determine the y-intercept.

y = 3.5x + b Insert x₁ and y₁

7 = 3.5×2 + b

7 = 7 + b Subtract 7 from each side

b = 0

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Step 3. Write the equation

y = mx + b

y = 3.5x + 0

y = 3.5x

The equation is y = 3.5x.