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r-ruslan [8.4K]

3 years ago

10

The table shows the height of a plant as it grows. What equation in point-slope form gives the plant’s height at any time? Let y

stand for the height of the plant in cm and let x stand for the time in months. time (months): 3,5,7,9 Plant height (cm): 15, 25, 35,45
A. y-15= (x-3)
B, y-15= 5(x-3)

1 answer:

dimulka [17.4K]3 years ago

3 0

Let's calculate the slope first:
m = y2-y1 / x2-x1
m = 25 - 15 / 5 -3
m = 10 /2
m = 5

Now, we know, y - y1 = m(x - x1)
y - 15 = 5(x - 3)

In short, Your Answer would be Option B

Hope this helps!

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<h3>1.</h3>

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

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The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
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The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

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$(1 + 2\, d)^{2} = 1 + 12\, d$ .

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These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

<h3>2.</h3>

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