1. Do Now Graph the linear function. y = 2x + 4 Course 2 5-3 Slope and Rates of Change Hwk: p 44

2. EQ: How do I determine the slope of a line and to recognize constant and variable rates of change? Course 2 5-3 Slope and Rates of Change M7A3.a Plot points on a coordinate plane; M7A3.b Represent, describe, and analyze relations from tables, graphs, and formulas

3. Vocabulary slope Insert Lesson Title Here Course 2 5-3 Slope and Rates of Change

4. The slope of a line is a measure of its steepness and is the ratio of rise to run: y If a line points downward as x increases, its slope is negative. If a line points upward as x increases, its slope is positive. x Run Rise Course 2 5-3 Slope and Rates of Change

5. Tell whether the slope is positive or negative. Then find the slope. Additional Example 1A: Identifying the Slope of the Line Course 2 5-3 Slope and Rates of Change The line rises from left to right. The slope is positive.

6. Tell whether the slope is positive or negative. Then find the slope. Additional Example 1A Continued The rise is 3. The run is 3. slope = rise run = 3333 =1 3 3 Course 2 5-3 Slope and Rates of Change

7. Tell whether the slope is positive or negative. Then find the slope. Additional Example 1B: Identifying the Slope of the Line Course 2 5-3 Slope and Rates of Change The line falls from right to left. The slope is negative. 0 2 2 –2 y x

8. Tell whether the slope is positive or negative. Then find the slope. Additional Example 1B Continued The rise is 2. The run is -3. slope = rise run = 2 -3 2 Course 2 5-3 Slope and Rates of Change 0 2 2 –2 y x

9. Check It Out: Example 1A The line does not point upward or downward so it is not positive or negative. Course 2 5-3 Slope and Rates of Change Tell whether the slope is positive or negative. Then find the slope.

10. Check It Out: Example 1A Continued The rise is 0. The run is 2. slope = rise run = 0202 =0 M(1, –1) N(3, –1) 2 Course 2 5-3 Slope and Rates of Change Tell whether the slope is positive or negative. Then find the slope.

11. Check It Out: Example 1B Insert Lesson Title Here (0, –4) (–2, 4) 8 –2 The rise is 8. The run is –2. slope = rise run = 8 –2 =–4 Tell whether the slope is positive or negative. Then find the slope. The line falls from left to right. The slope is negative. Course 2 5-3 Slope and Rates of Change

12. You can graph a line if you know its slope and one of its points. Course 2 5-3 Slope and Rates of Change

13. Use the slope  and the point (1, –1) to graph the line. Additional Example 2A: Using Slope and a Point to Graph a Line 2121 From point (1, 1) move 2 units down and 1 unit right, or move 2 units up and 1 unit left. Mark the point where you end up, and draw a line through the two points. y x –4 4 4 0 2 2 –2 = or rise run -2 1 2 ● ● Course 2 5-3 Slope and Rates of Change

14. Course 2 5-3 Slope and Rates of Change You can write an integer as a fraction by putting the integer in the numerator of the fraction and a 1 in the denominator. Remember!

15. Use the slope and the point (–1, –1) to graph the line. Additional Example 2B: Using Slope and a Point to Graph a Line 1212 From point (–1, –1) move 1 unit up and 2 units right. Mark the point where you end up, and draw a line through the two points. y x –4 4 4 0 2 2 –2 = rise run 1 2 ● Course 2 5-3 Slope and Rates of Change

16. Use the slope  and the point (2, 0) to graph the line. Check It Out: Example 2A 2323 From point (2, 0) move 2 units down and 3 units right, or move 2 units up and 3 unit left. Mark the point where you end up, and draw a line through the two points. y x –4 4 4 0 2 2 –2 = or rise run -2 3 2 -3 ● ● Course 2 5-3 Slope and Rates of Change

17. Use the slope and the point (–2, 0) to graph the line. Check It Out: Example 2B 1414 From point (–2, 0) move 1 unit up and 4 units right. Mark the point where you end up, and draw a line through the two points. y x –4 4 4 0 2 2 –2 = rise run 1 4 ● Course 2 5-3 Slope and Rates of Change

18. The ratio of two quantities that change, such as slope, is a rate of change. A constant rate of change describes changes of the same amount during equal intervals. A variable rate of change describes changes of a different amount during equal intervals. The graph of a constant rate of change is a line, and the graph of a variable rate of change is not a line. Course 2 5-3 Slope and Rates of Change

19. Tell whether each graph shows a constant or variable rate of change. A.B. Additional Example 3: Identifying Rates of Change in Graphs The graph is nonlinear, so the rate of change is variable. The graph is linear, so the rate of change is constant. Course 2 5-3 Slope and Rates of Change

20. Check It Out: Example 3 Insert Lesson Title Here Tell whether each graph shows a constant or variable rate of change. A.B. The graph is nonlinear, so the rate of change is variable. The graph is linear, so the rate of change is constant. y x –4 4 4 0 2 2 –2 y x –4 4 4 0 2 2 –2 Course 2 5-3 Slope and Rates of Change

21. The graph shows the distance a monarch butterfly travels overtime. Tell whether the graph shows a constant or variable rate of change. Then find how fast the butterfly is traveling. Additional Example 4: Using Rate of Change to Solve Problems Course 2 5-3 Slope and Rates of Change

22. Additional Example 4 Continued The graph is a line, so the butterfly is traveling at a constant rate of speed. The amount of distance is the rise, and the amount of time is the run. You can find the speed by finding the slope. slope (speed) = rise (distance) run (time) = 20miles 1 hour The butterfly travels at a rate of 20 miles per hour. Course 2 5-3 Slope and Rates of Change

23. Check It Out: Example 4 The graph shows the distance a jogger travels over time. Is he traveling at a constant or variable rate. How fast is he traveling? Insert Lesson Title Here 714212835 Time (min) 1 2 3 4 5 6 Distance (mi) 714212835 Time (min) 1 2 3 4 5 6 Distance (mi) 1 7 7 1 Course 2 5-3 Slope and Rates of Change

24. Check It Out: Example 4 Continued Insert Lesson Title Here The graph is a line, so the jogger is traveling at a constant rate of speed. slope (speed) = rise (distance) run (time) = 1 mi 7 min The jogger travels at a rate of 1 mile every 7 minutes. The amount of distance is the rise, and the amount of time is the run. You can find the speed by finding the slope. Course 2 5-3 Slope and Rates of Change

25. TOTD 1. Tell whether the slope is positive or negative. Then find the slope. Negative; -1 Insert Lesson Title Here Course 2 5-3 Slope and Rates of Change

26. TOTD 2. Use the slope and the point (–2, –3) to graph the line. Insert Lesson Title Here 1212 Course 2 5-3 Slope and Rates of Change

27. TOTD 3. Tell whether the graph shows a constant or variable rate of change. Insert Lesson Title Here Course 2 5-3 Slope and Rates of Change variable