Five-Minute Check (over Lesson 2–4) CCSS Then/Now New Vocabulary Key Concept: Scatter Plots Example 1: Real-World Example: Use a Scatter Plot and Prediction Equation Example 2: Real-World Example: Regression Line Over Lesson 2–4 Write an equation in slope-intercept form for the line with slope = A. B. C. D. , passing through (0, 1). Over Lesson 2–4 Write an equation in slope-intercept form for the line with slope = –1, passing through A. B. C. D. Over Lesson 2–4 What is the slope-intercept form of 4x + 8y = 11? A. 4x + 8y – 11 = 0 B. y = 4x – 11 C. D. Over Lesson 2–4 Write an equation in slope-intercept form of a line that passes through (1, 1) and (0, 7). A. 6x – y = 7 B. y = –6x + 7 C. x – 7y = 1 D. y = x + 7 Over Lesson 2–4 A plumber charges a flat fee of $65, and an additional $35 per hour for a service call. Write an equation that represents the charge y for a service call that lasts x hours. A. y = 35x + 65 B. 65 = 35x + y C. y = 65x + 35 D. total = 35x + 65y Over Lesson 2–4 What is the equation of a line that passes through the point (6, –4) and is perpendicular to the line with the equation A. e B. e C. e D. e Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Mathematical Practices 4 Model with mathematics. 5 Use appropriate tools strategically. You wrote linear equations. • Use scatter plots and prediction equations. • Model data using lines of regression. • bivariate data • regression line • scatter plot • correlation coefficient • dot plot • positive correlation • negative correlation • line of fit • prediction equation Use a Scatter Plot and Prediction Equation A. EDUCATION The table below shows the approximate percent of students who sent applications to two colleges in various years since 1985. Make a scatter plot of the data and draw a line of fit. Describe the correlation. Use a Scatter Plot and Prediction Equation Graph the data as ordered pairs, with the number of years since 1985 on the horizontal axis and the percentage on the vertical axis. The points (3, 18) and (15, 13) appear to represent the data well. Draw a line through these two points. Answer: The data show a strong negative correlation. Use a Scatter Plot and Prediction Equation B. Use two ordered pairs to write a prediction equation. Find an equation of the line through (3, 18) and (15, 13). Begin by finding the slope. Slope formula Substitute. Simplify. Use a Scatter Plot and Prediction Equation Point-slope form Substitute. Distributive Property Simplify. Answer: One prediction equation is Use a Scatter Plot and Prediction Equation C. Predict the percent of students who will send applications to two colleges in 2010. The year 2010 is 25 years after 1985, so use the prediction equation to find the value of y when x = 25. Prediction equation x = 25 Simplify. Answer: The model predicts that the percent in 2010 should be about 8.83%. Use a Scatter Plot and Prediction Equation D. How accurate is this prediction? Answer: Except for the point at (6, 15), the line fits the data well, so the prediction value should be fairly accurate. A. SAFETY The table shows the approximate percent of drivers who wear seat belts in various years since 1994. Which shows the best line of fit for the data? A. B. C. D. B. The scatter plot shows the approximate percent of drivers who wear seat belts in various years since 1994. What is a good prediction equation for this data? Use the points (6, 71) and (12, 81). A. B. C. D. C. The equation represents the approximate percent of drivers y who wear seat belts in various years x since 1994. Predict the percent of drivers who will be wearing seat belts in 2010. A. 83% B. 87% C. 90% D. 95% D. How accurate is the prediction about the percent of drivers who will wear seat belts in 2010? A. There are no outliers so it fits very well. B. Except for the one outlier the line fits the data very well. C. There are so many outliers that the equation does not fit very well. D. There is no way to tell. Page 96, 98 #3 – 6, 23 – 25, 30, 32