LESSON 5 3 Linear Relationships and Bivariate Data

LESSON 5. 3 Linear Relationships and Bivariate Data How can you contrast linear and nonlinear sets of bivariate data?

ADDITIONAL EXAMPLE 1 The charge for a cheese pizza changes as the number of toppings changes. Show that the relationship is linear, and then find the equation for the relationship. A line passes through all the graphed points so the relationship is linear. y = 1. 5 x + 8

ADDITIONAL EXAMPLE 2 The graph shows the distance of a train from a landmark as it travels at a constant speed. Use the graph to predict what the distance will be after 7. 5 hours. 400 miles

5. 3 LESSON QUIZ 8. 5. C, 8. 5. D, 8. 5. I 1. Does this table represent a linear relationship? Why or why not? No, the slope is not the same between 2 and 3 and between 3 and 4. 2. Change one value in this table so that this table does represent a linear relationship. Change y to 11 for x = 3.

Explain whether or not each relationship is linear. 3. The number of inches in a student’s height and the height in feet Yes, the rate of change is a constant 12 inches per foot. 4. The radius of a circle and its area No; the rate of change is not constant.

Explain whether or not each relationship is linear. 5. An amusement park charges a price for admission and a price for each ride. Joe spent $10. 50 and went on 4 rides. Janie spent $14. 25 and went on 9 rides. Write a linear equation for the amount spent and predict the amount you would spend to go on 17 rides. a = 0. 75 r + 7. 5; $20. 25

How can you contrast linear and nonlinear sets of bivariate data? The graph of a linear set of data is a single line; the graph of a nonlinear set of data is not a single line.