Question

The linear function graphed below represents the height of a stalk of corn since a farmer began using a new fertilizer. What is the initial value?

A graph titled Height of a Stalk of Corn has Number of Days Using New Fertilizer on the x-axis and Height (feet) on the y-axis. Points are at (3, 10), (4, 12), (5, 14), and (6, 16).

Answer 1

SOLUTION

GIVEN

The linear function graphed below represents the height of a stalk of corn since a farmer began using a new fertilizer.

A graph titled Height of a Stalk of Corn has Number of Days Using New Fertilizer on the x-axis and Height (feet) on the y-axis. Points are at (3, 10), (4, 12), (5, 14), and (6, 16).

TO DETERMINE

The initial value

EVALUATION

Here it is given that The linear function graphed below represents the height of a stalk of corn since a farmer began using a new fertilizer

Let y = ax + b is the linear function

Now (3, 10), (4, 12) satisfies the equation

$\therefore \sf{ \: \: 3a + b = 10 \: \: \: - - - (1)}$

$\therefore \sf{ \: \: 4a + b = 12 \: \: \: - - - (2)}$

Equation (2) - Equation (1) gives

a = 2

Equation (1) gives

b = 10 - 6 = 4

So the linear function is

$\sf{y = 2x + 4}$

Now initially x = 0

Which gives

$\sf{ y =( 2 \times 0) + 4}$

$\therefore \sf{ \: \: y = 4}$

So the initial value is x = 0 , y = 4

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Answer 2

Answer:

4 feet

Step-by-step explanation: