Question

Number of months

Height of plant (inches)
1
2
3
4
2.3
3.6
5.2
4.9
5
7.3
6
7.6
7
8.0
a) What is the equation of the line of best fit? How tall can we expect the plant to be after 13 months?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line of best fit, we can use the linear regression function in a graphing calculator or a statistical software. However, since we only have a small amount of data, it may be more appropriate to visually estimate the line of best fit:

Month (x) Height (y)
-----------------------------
1 2.3
2 3.6
3 5.2
4 4.9
5 7.3
6 7.6
7 8.0

By plotting these points on a graph and drawing a line that roughly approximates the trend, we find that the line passes through the point (1, 2.3) and (7, 8.0). It has an upward slope, suggesting that as the number of months increases, the height of the plant also increases.

The slope (m) of the line can be found using the formula:

m = (change in height) / (change in months)

m = (8.0 - 2.3) / (7 - 1) = 5.7 / 6 = 0.95

The y-intercept (b) of the line can be found using the formula:

b = y - mx

Using the point (1, 2.3),

b = 2.3 - (0.95 * 1) = 2.3 - 0.95 = 1.35

Therefore, the equation of the line of best fit is:

y = 0.95x + 1.35

To find the height of the plant after 13 months, we can substitute x = 13 into the equation:

y = 0.95(13) + 1.35

y = 12.35 + 1.35

y = 13.7

Therefore, we can expect the plant to be approximately 13.7 inches tall after 13 months.