Questions: Plot the data and label the graph. Seeding Height (cm): 9, 14, 16, 20, 38, 42, 54, 62 Day: 5, 8, 12, 16, 22, 25, 28, 30 1. Draw a trend line to represent the data. 2. Find the slope of the trend line. 3. Estimate the y-intercept of the trend line. 4. Write an equation to describe the trend line. 5. Use the equation to predict the seedling height on day 45.

Plot the data and label the graph. Seeding Height (cm): 9, 14, 16, 20, 38, 42, 54, 62 Day: 5, 8, 12, 16, 22, 25, 28, 30 1. Draw a trend line to represent the data. 2. Find the slope of the trend line. 3. Estimate the y-intercept of the trend line. 4. Write an equation to describe the trend line. 5. Use the equation to predict the seedling height on day 45.
Transcript text: Plot the data and label the graph. \begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline Seeding Height (cm) & 9 & 14 & 16 & 20 & 38 & 42 & 54 & 62 \\ \hline Day & 5 & 8 & 12 & 16 & 22 & 25 & 28 & 30 \\ \hline \end{tabular} 1. Draw a trend line to represent the data. 2. Find the slope of the trend line. 3. Estimate the $y$-intercept of the trend line. 4. Write an equation to describe the trend line. 5. Use the equation to predict the seedling height on day 45 .
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Solution

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Solution Steps

Step 1: Draw a trend line to represent the data

To draw a trend line, we can use linear regression to find the best-fit line for the given data points.

Step 2: Find the slope of the trend line

Using linear regression, the slope \( m \) of the trend line is calculated as follows: \[ m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} \] where \( n \) is the number of data points, \( x \) represents the days, and \( y \) represents the seeding height.

Step 3: Estimate the \( y \)-intercept of the trend line

The \( y \)-intercept \( b \) is calculated using: \[ b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2} \]

Final Answer

The slope \( m \) and \( y \)-intercept \( b \) are used to form the equation of the trend line: \[ y = mx + b \]

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 70, "ymin": 0, "ymax": 70}, "commands": ["y = (0.8571)x + 1.4286"], "latex_expressions": ["$y = 0.8571x + 1.4286$"]}

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