# Lesson 11.4 Scatter Plots & Slope Intercept Form  Learn to determine the correlation of a scatter plot and find the slope of linear equations using the Slope Intercept Formula.

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## About Lesson 11.4 Scatter Plots & Slope Intercept Form

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1. Lesson 11.4: Scatter Plots Lesson 11.4: Scatter Plots Objective: Determine the correlation of a scatter plot

2. Warm Up 1. What is the slope of a line that passes through points with coordinates (-2,-6) and (-4, -5)? a. -2 b. - 1/2 c. 1/2 d. 2 2. Given that the Slope Intercept Formula is y = mx + b, and remembering that m = the slope, give the slope of the following linear equations: a. y = -3x + 5 b. y = 3/5x + 7 c. y = 4x - 3 3. What is the slope of the equation 3x + 2y = 6? (Hint: Solve for y. This will give you the Slope Intercept Form)

3. Scatter Plot Scatter Plot • A scatter plot is a graph of a collection of ordered pairs (x,y). • The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

4. Positive Correlation Positive Correlation • If the x-coordinates and the y-coordinates both increase, then it is POSITIVE CORRELATION. • This means that both are going up, and they are related.

5. Positive Correlation Positive Correlation • If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation. Age 1 2 3 4 5 6 7 8 Height “ 25 31 34 36 40 41 47 55

6. Negative Correlation Negative Correlation • If the x-coordinates and the y- coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION. • This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

7. Negative Correlation Negative Correlation • If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation. Age of car 1 2 3 4 5 Value \$30,000 \$27,000 \$23,500 \$18,700 \$15,350

8. No Correlation No Correlation • If there seems to be no pattern, and the points looked scattered, then it is no correlation. • This means the two are not related.

9. No Correlation No Correlation • If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

10. Scatterplots Which scatterplots below show a linear trend? a) c) e) b) d) f) Negative Correlation Positive Correlation Constant Correlation

11. Year Sport Utility Vehicles (SUVs) Sales in U.S. Sales (in Millions) 1991 1992 1993 1994 1995 1996 1997 1998 1999 0.9 1.1 1.4 1.6 1.7 2.1 2.4 2.7 3.2 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5 4 3 2 1 Objective - To plot data points in the coordinate plane and interpret scatter plots.

12. 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5 4 3 2 1 Trend is increasing. Scatterplot - a coordinate graph of data points. Trend appears linear. Positive correlation. Predict the sales in 2001.

13. Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis.. Student Time Spent Watching TV Time Spent on Homework Sam Jon Lara Darren Megan Pia Crystal 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 180 min. 150 min. 90 min. 30 min. 90 min. 90 min. 90 min.

14. Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. TV Homework 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 180 min. 150 min. 90 min. 30 min. 120 min. 120 min. 90 min. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30

15. Describe the relationship between time spent on homework and time spent watching TV. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30 Trend is decreasing. Trend appears linear. Negative correlation.