1. Moving Straight Ahead Investigation 1.2 Walking Rates & Linear Relationships Learning Target: I can represent linear relationships using tables, graphs, and equations. Homework: 1) Complete pg. 6 for MSA 1.2 2) Correct online with the Zaption Review video. Warm Up: Christine walks 1.5 meters per second. a)How long would it take her to walk 300 meters? b)Write an equation to represent the distance d in meters that Christine could walk in t seconds if she maintained that pace. a)How far would she walk in 75 seconds?

2. Warm Up: Christine walks 1.5 meters per second. a)How long would it take her to walk 300 meters? b)Write an equation to represent the distance d in meters that Christine could walk in t seconds if she maintained that pace. c)How far would she walk in 75 seconds? 1.5 m. 1 sec. = 300 m. x sec. d = 1.5 t d = 1.5(75) 112.5 = 1.5(75) 112.5 meters in 75 seconds 200 sec.

3. The walking rate is the amount that the distance (in meters) for each person is changing as time increases by 1 second. 1. Complete the table showing the distance walked by each student for the first ten seconds. MSA 1.2 packet p. 4

4. How does the walking rate appear as a pattern in the table? Alana’s walking rate is 1m/sec. As time increases by 1 second, the distance increases by 1 meter. 1. Complete the table showing the distance walked by each student for the first ten seconds.

5. 2. Graph the times and distances for the three students on the same coordinate axes. Use a different color for each student’s data. KEY Leanne Gilberto Alana Distance (meters) Time (seconds) Walking Rates

6. The greater the walking rate, the steeper the line on the graph. (or greater slope) How does the walking rate affect the graph? Walking Rates Time (seconds) Distance (meters)

7. What is the starting point for each student? This is called the y-intercept. What is the rate of change for each student? This is called the slope. What does the point (6,12) represent? Whose line is it on? Whose line are these points on? (9,9) (5,12.5) What is the starting point for each student? This is called the y-intercept. What is the rate of change for each student? This is called the slope. What does the point (6,12) represent? Whose line is it on? Whose line are these points on? (9,9) (5,12.5)

8. The walking rate is represented as the number that time is multiplied by to get the distance. This is the number in front of the variable. It is called the coefficient or the slope. 3. Write an equation that gives the relationship between the time t and the distance d walked for each student. Alana: 1d = 1t or d = t or y = 1x + 0 or y = x Gilberto: 1d = 2t d = 2t y = 2x + 0 y = 2x Leanne: 1d = 2.5t d = 2.5t y = 2.5x + 0 y = 2.5x How is the walking rate represented in the equations?

9. In the table: For every increase of 1 unit in x, the value of y increases by a constant amount. In each equation: It is of the form y = mx Which represents a proportional relationship. And in the graph? In the graph: A proportional relationship is a straight line that passes through the origin (0,0).

10. All three: Table, Equation, Graph are proportional. They are all of the form d = rt The constant of proportionality is the value of r for each relationship. (Also called the coefficient or the slope)

11. Alana: increases by 1 m Gilberto : increases by 2 m Leanne: increases by 2.5 m In the table it is found as the difference between the values for distance.

12. In the graph it is the steepness of the line. As x (time) increases by 1 y (distance) goes up 1 for Alana 2 for Gilberto 2.5 for Leanne.

13. And in the equations? Alana: y = x 1 = 1(1) 2 = 1(2) 5 = 1(5) Gilberto: y = 2x y = 2(1) 4 = 2(2) 10 = 2(5) Leanne: y = 2.5x 1 = 2.5(1) 5 = 2.5(2) 12.5 = 2.5(5)

14. If t increases by 5 seconds: Alana: d increases by 5 m. Gilberto: d increases by 10 m. Leanne: d increases by 12.5 m. In a table: As x increases by 5, find the difference in y values.

15. Walking Rates Time (seconds) Distance (meters) The difference in y-coordinates of two points on the line whose difference in x-coordinates is 5. In a graph:

16. And in the equations? Alana: 5 = 1(5) Gilberto: 10 = 2(5) Leanne: 12.5 = 2.5(5) y = mx d = __t

17. Walking rates per minute: (walking rate per sec x 60 sec) Alana: 60 meters/min Gilberto: 120 meters/min Leanne: 150 meters/min Walking rates per hour: (walking rate per min x 60 min) Alana: 3,600 m/min Gilberto: 7,200 m/min Leanne: 9,000 m/min

18. Moving Straight Ahead Investigation 1.2 Walking Rates & Linear Relationships Did I meet my Learning Target? I can represent linear relationships using tables, graphs, and equations. Homework: 1) Complete pg. 6 for MSA 1.2 2) Correct online with the Zaption Review video.

19. George = No Elizabeth = Yes! Constant rate 3m/2s Billie = Yes! Constant rate 2.25 m/s Bob = No HOMEWORK: