1. Linear FunctionFunction where the graph is a lineChanges by a constant amount at set intervals

2. Slope  a fraction that tells the slant of a line

3. Big slopeSmall slope

4. Positive slopeNegative slope

5. Zero slopeUndefined (or infinite) slope

6. Slope

9. If you know two points on a line, you can find the slope by using this formula:

10. Example: Find the slope of the line through (3,5) and (7,10).

11. Find the slope of the line through (4,9) and (-1,12)

13. It’s easy to use slope to graph linear functions.

14. If a function is written in the form y = mx + b or f(x) = mx + b …m (the number by x) is the slopeb (the number by itself) is the y-intercept, the place where the line crosses the y-axis.

15. EXAMPLE: Graph

17. Graph y = –2x + 3

18. Graph y = –2x + 3 The y-intercept is 3

19. Graph y = –2x + 3 The y-intercept is 3 The slope is -2 or -2 / 1 … down 2, over 1

21. You can also graph lines by using the intercepts (the places where x and y = 0) Plug in 0 for each variable, and see what the other one is.

22. EXAMPLE: Graph 2x – 5y = -10

23. EXAMPLE: Graph 2x – 5y = -10 x = 0 … 2(0) – 5y = -10 -5y = -10 y = 2 (0,2) is the y-intercept.

24. EXAMPLE: Graph 2x – 5y = -10 y = 0 … 2x – 5(0) = -10 2x = -10 x = -5 (-5,0) is the x-intercept.

25. EXAMPLE: Graph 2x – 5y = -10

26. Horizontal and Vertical Lines

27. Horizontal linesSlope = 0… So, can be written in the form y = 0x + bThis simplifies to just y = bWhenever an equation says y = #, the graph is a horizontal line through that number.

28. Example: Graph y = -2

29. Graph y = 3

30. Vertical linesSlope is undefinedThese are the only lines that CAN’T be written in the form y = mx + b.Vertical lines always have equations of the form x = #.

31. Graph x = 3

32. Graph x = -2

33. y = # … horizontal x = # … vertical