Monday October 3 rd

1. Monday October 3rd Wrap up of Chapter 3 -some people need to take Ch 3 test -some need to finish Ch 3 test -others can work on extra credit 3.8 chapter review

2. Chapter 4 Graphing Linear Equations4.1 Coordinates and Scatter Plots

3. Label axes Label scale Example 1: Plot and label the points: A(2,1), B(5,03), C(-3,0), D(-2,-2), E(0,4), F(-2,3)

4. Example 2: The data below represent the weight and height of a male. At age 13, he was 63 in. tall. Predict his weight at age 13.

9. How can we graph an equation? 4.2 Graph an equation by using a table of values 4.3 Graphing Using Intercepts 4.6 Graphing Using Slope Intercept Form: y=mx+b

10. Find the x and y intercepts of 4x+3y=12 Solution: 4x + 3(0) = 12 (substitute 0 for y) 4x = 12 x = 3 The x intercept is 3. The line crosses the x axis at (3,0). 4(0) + 3y = 12 (substitute 0 for x) 3y = 12 y = 4 The y intercept is 4. The line crosses the y axis at (0,4). Use the intercepts to graph the line. By sure to label your axes and mark your scale.

11. Graph x – 2 =4y Solution: x – 2 = 4(0) (substitute 0 for y) x – 2 = 0 The x intercept is 2. The line crosses the x axis at (2,0). 0 – 2 = 4y (substitute 0 for x) -2 = 4y y = - 1/2 The y intercept is -1/2. The line crosses the y axis at (0,-1/2). Use the intercepts to graph the line. By sure to label your axes and mark your scale.

12. Graph y = -2x + 25 Solution: 0 = -2x +25 (substitute 0 for y) 2x = 25 x = 12 1/2 The x intercept is 12 1/2 The line crosses the x axis at (12.5,0) y = -2(0) + 25 (substitute 0 for x) y = 25 The y intercept is 25. The line crosses the y axis at (0,25). What is you scale for graphing the line?

13. Monday October 10th Bellwork: p224 #1, 5, 11 • Plot and label the ordered pairs in a coordinate plane: A(-4,1), B(0,2), C(-3,0)

14. Find three different ordered pairs that are solutions of the equation. Graph the equation. P 224 #5) y=2x-6

15. Find the x and y intercept of the line. Graph the line. Lable the intercepts. 11) y=4-x y=4-0 (insert 0 for x to find y intercept) y=4 y intercept= (0,4) 0=4-x (insert 0 for y to find x intercept) x=4 x intercept = (4,0)

17. 4.4 The Slope of a Line

18. Given (x1,y1) and (x2,y2), find slope using m = y2-y1 x2-x1 1. Find the slope of the line passing through (-3,0) and (-1,6)

19. Given (x1,y1) and (x2,y2), find slope using m = y2-y1 x2-x1 2. Find the slope of the line passing through (-1,-3) and (5,-3)

20. Given (x1,y1) and (x2,y2), find slope using m = y2-y1 x2-x1 3. Find the slope of the line passing through (-2,1) and (1,-3)

21. Given (x1,y1) and (x2,y2), find slope using m = y2-y1 x2-x1 4. Find the slope of the line passing through (0,-1) and (0,4)

22. Key concepts from 4.4 Given (x1,y1) and (x2,y2), find slope using m = y2-y1 x2-x1

24. Why is slope important?

25. Goals for today: 4.5 Direct variation Review for Friday quiz 4.1-4.5 Two variables vary directly if k not = 0 and y=kx Think direct variation (y=kx) indirection variation (y=k/x) k=constant of variation, also the slope

26. Ex.1) Find the constant of variation and the slope for the direct variation model y=-3x y=kx k=constant so k=-3 • Ex. 2) The variables x and y vary directly. When x=-3, y=-30 • Write an equation that relates x and y • y=kx -30=k(-3) k=10 • y=10x • b) Find the value of y when x=8 • y=10x y=10(8) y=80

27. Ex 3) The income at a store varies directly as the advertising budget. When the owner spent $3000 per month on advertising, the monthly gross income was $120,000. If the owner increases the advertising budget to $5000, how much gross income should they expect? y=kx let x=$advertising and y=$gross 120,000=k(3000) k=40 y=40x If x=$5000, then: y=40(5000) y=$200,000 Or if 3000 = 5000 ,then 3000y=60,000,000 y=$200,000 120000 y

28. Monday, October 17th Start of 2nd quarter

29. Chapter 4 Graphing Linear Equations4.1 Coordinates and Scatter Plots

30. How can we graph an equation? 4.2 Graph an equation by using a table of values 4.3 Graphing Using Intercepts 4.6 Graphing Using Slope Intercept Form: y=mx+b

31. Key concepts from 4.4 Given (x1,y1) and (x2,y2), find slope using m = y2-y1 x2-x1

32. 4.5 Direct variation Two variables vary directly if k not = 0 and y=kx Think direct variation (y=kx) indirection variation (y=k/x) k=constant of variation, also the slope

34. 4.6 Graphing Using Slope Intercept Form

35. Ex 1) Write the equation 3x + 4y =8 in slope-intercept form. Identify the slope and y-intercept. 3x + 4y = 8 -3x+4y = 8-3x 4y= -3x +8 y=(-3/4)x +2 Slope = -3/4 Y-intercept = 2

36. Ex 2) Graph -2x + y = 5 +2x+ y = 5 + 2x y= 2x + 5 slope = 2 y-intercept =5

37. Ex 3) Which of the following lines are parallel? • 3y= -9x -5 • 2y-6x= -5 • 12x +4y =1 • y= -3x –(5/3) • 2y=6x -5 y=3x –(5/2) • 12x + 4y = 1 4y= -12x + 1 y= -3x + ¼ a) And c) are parallel because their slopes are the same.

40. 4.7 Solving Linear Equations Using Graphs

43. 5x+ 3 = -2 5x = -2 -3 5x = -5 x= -1 5x +3 +2 = -2+2 5x + 5 = 0 y= 5x + 5 Slope = 5 y-intercept = 5 When plug in 0 for y, then x = -1.

45. 4.8 Functions and Relations Relation: any set of ordered pairs Function: for every input, there is exactly one output

46. Function notation: f(x) Instead of: y=2x+4 f(x) = 2x+4 When we plug in 1 for x what do we get? f(1) = 2(1) +4 f(1) = 6

48. Evaluating a function for specific inputs:

50. 32. f(x)= -2x+5 Think of it like: y= -2x+5 Slope = -2 y-intercept = 5