Chapter 4 Graphing

1. Chapter 4 Graphing Graph of a Linear Function

2. Linear Function • Fencing Company: • Fixed Charge for a Chain Link Fence Project • $125 • The rest of the cost for a 4 ft high fence is based on $8.50 per lineal foot of fencing. • A 6 ft high fence would be based on $13.00/ft Cost = $125 + $8.50(Length) Cost = $125 + $13.00(Length)

3. Cost = $125 + $8.50(Length) Cost = $125 + $13.00(Length)

4. run rise Slope • Slope – a ratio that describes the steepness of a line and the direction that it slants. y 2 units  3 units  x

5. Slope Slope is relatively large & positive. y • Slope – a ratio that describes the steepness of a line and the direction that it slants. Slope is relatively “large” & negative. Slope is relatively “small” & negative. Slope is relatively small & positive. x

6. run rise Compute Slope when two points are known. • Slope formula:  

7.   Compute Slope • Compute the slope of this line. y 4 – 0 4 – 3 x 0 – 4 3 – 4

8.   Compute Slope • Compute the slope of this line. y 4 – (-1) -2 – 1 x -1 – 4 1 – (-2)

9. Compute Slope • Compute the slope of a line that passes through these two points. • (-2,3) and (-6,5) -2 3 -6 5 - -

10.   Horizontal Lines • Compute the slope of this line. y y = 2 2 – 2 = 0 5 – (- 3) x

11.   Vertical Lines • Compute the slope of this line. y x = 4 5 – (- 3) = Undefined 4 - 4 x

12. Summary • Horizontal lines: • Slope = 0 • Vertical lines: • Slope = Undefined  0  0

13. Use Intercepts to Graph Lines

14. Intercepts y • Intercepts – locations where a graph intersects with an axis. (0,5)  y - intercept x - intercept  x (-6,0)

15. Matching Excercise Intercepts y  x - intercept y - intercept (0,10) (8,0)  x

16. Graph with Intercepts • Graph using intercepts. 3x + 2y = 12 In every x-intercept, y = 0 (4,0) 3x + 2(0) = 12   3x = 12 x = 4

17. Graph with Intercepts • Graph using intercepts. 3x + 2y = 12 (0,6)   In every y-intercept, x = 0 (4,0) 3(0) + 2y = 12  2y = 12 y = 6

18. Compute Intercepts • Compute the x and y intercepts of this equation. 4x – 3y = 24 y – intercept x – intercept (0, y) (x, 0) ( 0,-8 ) ( 6,0 ) 4(0) – 3y = 24 4x – 3(0) = 24 -3y = 24 4x = 24 y = -8 x = 6

19. Slope Intercept Form

20. y x Introduction 1 of 2 4→ • Graph the line that passes through the point (0,2) and has a slope of m =  3↑ (0,2)  y-intercept

21. y x Introduction 2 of 2 • Graph the line that passes through the point (0,-1) and has a slope of m = (0,-1)  y-intercept -2↓  3→

22. Slope-Intercept Form • Equations like these… • …are in slope-intercept format.

23. Slope-Intercept Form 4  1 slope  y-intercept y-intercept = (0,2)

24. Slope-Intercept Form slope = 3 1  y-intercept = (0,-5) 3  y-intercept

25. Slope-Intercept Form slope y-intercept  -2 y-intercept = (0,-6)  3

26. Rewrite Linear Equations into Slope-Intercept Form

27. Rearranging Equations to Slope-Intercept Form 2x + y = 1 2x + y = 1 -2x -2x y = -2x + 1

28. Rearranging Equations to Slope-Intercept Form 2x + 3y = 9 2x + 3y = 9 -2x -2x 3y = -2x + 9 3 3 3

29. Rearranging Equations to Slope-Intercept Form -x -x x – 4y = 12 x – 4y = 12 -4y = -x + 12 -4 -4 -4

30. Homework • Textbook • Page 221 • 1-25 odd