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the table shows the height of a plant as it grows. A. Model the data with an equation. B. Based on your model, predict the height of tje plant at 12 months. Time (months), 3, 5, 7, 9. Plant height (cm), 9, 15, 21, 27.
A. Y-9=3/2(x-3);18 cm
B. Y-9=3(x-3);36 cm
C. The relationship cannot be modeled
D. Y-3=3/2(x-9);39 cm

Respuesta :

The answer is number B.
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Answer:

The equation which represents the given data is [tex]y-9=3(x-3)[/tex]and  the height of the plant at 12 months is 36 cm.

Step-by-step explanation:

Given :

Time (months)(x): 3, 5, 7, 9.

Plant height (cm)(y), 9, 15, 21, 27.

Solution:

We will use two point slope form to find the equation which represents the given situation.

Formula: [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex](x_1,y_1)=(3,9)[/tex]

[tex](x_2,y_2)=(5,15)[/tex]

Substitute the values in the given formula.

[tex]y-9=\frac{15-9}{5-3}(x-3)[/tex]

[tex]y-9=\frac{6}{2}(x-3)[/tex]

[tex]y-9=3(x-3)[/tex]

Now we are supposed to find the height after 12 months.

[tex]y-9=3(12-3)[/tex]

[tex]y-9=3(9)[/tex]

[tex]y-9=27[/tex]

[tex]y=36[/tex]

So, the equation which represents the given data is [tex]y-9=3(x-3)[/tex]and  the height of the plant at 12 months is 36 cm.

Thus Option B is correct.

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