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# Lesson 2 Homework Practice Use Trend Lines To Make Predictions Answer Key

## Lesson 2 Homework Practice Use Trend Lines To Make Predictions Answer Key

In this lesson, you will learn how to use trend lines to make predictions based on scatter plots. A trend line is a line that best fits the data points in a scatter plot. It shows the general direction and strength of the relationship between two variables. You can use a trend line to estimate the value of one variable given the value of another variable.

To draw a trend line, you can use a straightedge to draw a line that has about the same number of points above and below it. You can also use a graphing calculator or software to find the equation of the line that minimizes the sum of the squared errors. This is called the line of best fit or the least-squares regression line.

To use a trend line to make predictions, you can extend the line beyond the data points and find the corresponding value on the vertical axis for a given value on the horizontal axis, or vice versa. This is called interpolation if the value is within the range of the data, or extrapolation if the value is outside the range of the data.

Here are some examples of how to use trend lines to make predictions based on scatter plots.

## Example 1

The scatter plot below shows Lily's running data. She recorded the distance and time for each of her runs.

To draw a trend line, we can use a straightedge to draw a line that has about the same number of points above and below it. We can ignore any outliers, such as the point at (3, 40), which may be due to measurement errors or other factors.

To use the trend line to predict how long it would take for Lily to run 4.5 miles, we can draw a vertical line from 4.5 on the horizontal axis to the trend line, and then draw a horizontal line from there to the vertical axis. We can estimate that it would take about 45 minutes for Lily to run 4.5 miles.

## Example 2

The scatter plot below shows the relationship between the number of chapters and the total number of pages for several books.

To draw a trend line, we can use a graphing calculator or software to find the equation of the line that best fits the data. The equation is y = 10x + 10, where x is the number of chapters and y is the number of pages.

To use the trend line to predict the number of pages for 18 chapters, we can plug in x = 18 into the equation and solve for y. We get y = 10(18) + 10 = 190. We can estimate that a book with 18 chapters would have about 190 pages.