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1 What you will learn today 1. New vocabulary 2. How to determine if data points are related 3. How to develop a linear regression equation 4. How to graph a linear inequality

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 2 Correlation and Best-Fitting Lines Vocabulary: Scatter Plot is a graph used to determine whether there is a relationship between paired data (e.g. exercise and heart rate). It looks like a bunch of dots on a graph. Positive correlation:No Correlation Negative correlation:

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 3 Determining Types of Correlation Provided by Mrs. C.

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 4 Steps for Developing a “Best Fit Line” Step 1: Draw a scatter plot of the data (an accurate plot) Step 2: Sketch the line that appears to follow most closely the pattern of the points. There should be as many points above the line as below it. Step 3: Choose two points on the line and estimate the coordinates of each point. These points do not have to be from the original data set. Step 4: Find the equation of the line by finding the slope and using one of the linear equation forms.

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 5 Example The data pairs give the average speed of an airplane during the first 10 minutes of flight, with x in minutes and y in miles per hour. Approximate the best fit line for the data. (1, 180), (2, 250), (3, 290), (4, 310), (5, 400), (6, 420), (7, 410), (8, 490), (9, 520), (10, 510)

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 6 Homework for Section 2.5 Page 103, 8-10 all, 19, 20, 24, 25

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 7 Graphing Linear Inequalities How many solutions are there to the equation y < 2? We have to have a way to note this on a coordinate plane.

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 8 Graphing Linear Inequalities A linear inequality in two variables is an inequality that can be written in one of the following forms:Ax + By < C These inequalities have many solutions.

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 9 Example Check whether the given ordered pair is a solution of 2x + 3y > 5. A) (0, 1)B) (4, -1)C) (2, 1)

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 10 Graphing a y mx + b Inequality Steps: 1. Graph the boundary line just as you would in a y = mx + b equation. 2. Decide which side of the boundary line to shade by testing a point on either side of the boundary line.

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 11 Example Graph y < -2 and

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 12 Another Example Graph y < 2x and

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 13 You Try Graph 2x + 3y < 6

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Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities 14 Homework Page 111, 14, 16, 30, 31, 48, 49

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