1. 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

2. 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:

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

4. 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.

5. 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)

6. 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

7. 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.

8. 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.

9. 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)

10. 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.

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

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

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

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