Slope and y-intercept

1. Slope and y-intercept Lesson 8-3 p.397

2. Slope and y-intercepts • When studying lines and their graphs (linear equations), we can notice two things about each graph. • Slope—is the steepness of a line. • y-intercept—is the point where the line crosses the y-axis

3. Slope and y-intercept • Let’s start with the y-intercept. That is the easiest to identify: Notice the graph at the left. What is the point on the y-axis where the graph of the line crosses the y-axis?

4. Slope and y-intercept • Let’s start with the y-intercept. That is the easiest to identify: Notice the graph at the left. What is the point on the y-axis where the graph of the line crosses the y-axis? Yes, it crosses the y-axis at “2” We would say that the y-intercept is 2.

5. Slope and y-intercept • Let’s try another one. What is the y-intercept of this graph?

6. Slope and y-intercept • Let’s try another one. What is the y-intercept of this graph? Yes, it is -3.

7. Slope • Let’s look at some basic characteristics of slope. • If a line goes uphill from left to right, we say the slope is positive. • If the line goes downhill from left to right, we say the slope is negative.

8. Slope This is a positive slope. This is a negative slope.

9. Slope There are a couple of unusual situations. The graph on the left Has a slope of zero. This one is called undefined. Copy this down for now. . .the reason will be explained later.

10. Slope • Now let’s take a look at how to calculate slope. Write this down: slope = rise run To identify the slope of a line, we simply count lines up or down, (that is the rise) and count lines across (that is the run). Then we write our answer as a fraction. (ratio) Rise is vertical change (UP is positive, DOWN is negative) Run is horizontal change (RIGHT is positive , LEFT is negative)

11. Example Notice the two yellow points on the Line. Each one is identified as a Whole number ordered pair.

12. Example Notice the two yellow points on the Line. Each one is identified as a Whole number ordered pair. Starting from the lower point, we Rise 2 lines until we are even with The next point.

13. Example Notice the two yellow points on the Line. Each one is identified as a Whole number ordered pair. Starting from the lower point, we Rise 2 lines until we are even with The next point. Then we run 1 to reach the second Point. The rise = 2 and the run = 1.

14. Example Notice the two yellow points on the Line. Each one is identified as a Whole number ordered pair. Starting from the lower point, we Rise 2 lines until we are even with The next point. Then we run 1 to reach the second Point. The rise = 2 and the run = 1. In this case the slope or rise = 2 run 1 Or simply “2”

15. Try This • Name the slope of each line.

16. Try This • Name the slope of each line. Slope = 3 Slope = -1/5 2

17. Slope • There is another way to find the slope. • In the previous example we found the slope by counting lines on the coordinate plane. • If no picture is given, but instead 2 ordered pairs are given we can calculate the slope. • Copy this down: y2 – y1 = slope x2 – x1

18. Slope Consider the ordered pairs (3,2) and (7,5) The first ordered pair has the x1 and y1 3 2 The next onehas the x2 and y2 7 5 Substitute the numbers into the formula And then solve: y2 – y1 = slope x2 – x1 5 – 2 = 3 7 – 3 4

19. Try This • Using the slope formula, find the slope of the line that crosses through these points: • (8, -1) (0, -7) • (-4,3) (-10, 9)

20. Try This • Using the slope formula, find the slope of the line that crosses through these points: • (8, -1) (0, -7) 3 4 • (-4,3) (-10, 9)

21. Try This • Using the slope formula, find the slope of the line that crosses through these points: • (8, -1) (0, -7) 3 4 • (-4,3) (-10, 9) -1

22. 2-4-11 Agenda • PA# 14 • Pp.400-401 #1,3,5 11-21 odd

23. 2-5-10 • Please have out HW, red pen, and book. • Start correcting HW

24. 2-8-10 Agenda • PA# 15 • Workbook p.67 #1-10