2. Notes Chapter 3 Section 6 Write Linear Equations Essential Question WHY are graphs helpful? Vocabulary: point-slope form Common Core State Standards: 8.EE.8c

3. Activity – FSW 3.6

4. Page 221 What you will learn Take a minute to scan the lesson and predict two things you will learn about. 1. point-slope form 2. write a linear equation

5. Give an Example of Each Slope-intercept Form Standard Form And today Point-Slope Form

6. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 1. Is the relationship linear? Explain? Number of people, x 1234 Total Cost, y$13$22$31$40

7. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 1. Is the relationship linear? Explain? Yes, the rate of change is constant for every pair of points in the table! Number of people, x 1234 Total Cost, y$13$22$31$40 1 1 1 1 1 1 22-13=9 31-22=9 40-31=9

8. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 2. What is the slope of the related graph? Number of people, x 1234 Total Cost, y$13$22$31$40 1 1 1 1 1 1 22-13=9 31-22=9 40-31=9

9. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 2. What is the slope of the related graph? Difference in y’s over the difference in the x’s. 9/1 = 9 Number of people, x 1234 Total Cost, y$13$22$31$40 1 1 1 1 1 1 22-13=9 31-22=9 40-31=9

10. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 3. Choose an ordered pair then substitute the values in the equation y=mx+b. Number of people, x 1234 Total Cost, y$13$22$31$40

11. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 3. Choose an ordered pair then substitute the values in the equation y=mx+b. y = m x + b 22 = 9*2 + b Number of people, x 1234 Total Cost, y$13$22$31$40

12. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 4. Solve for b to find the y-intercept. 22 = 9*2 + b Number of people, x 1234 Total Cost, y$13$22$31$40

13. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 4. Solve for b to find the y-intercept. 22 = 9*2 + bmultiply 9 times 2 22 = 18 + b subtract 18 from both sides 4 = b y-intercept is 4 the point (0,4) Number of people, x 1234 Total Cost, y$13$22$31$40

14. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 5. Write an equation of the line in slope- intercept form (y=mx+b). Number of people, x 1234 Total Cost, y$13$22$31$40

15. Page 221 Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table 5. Write an equation of the line in slope- intercept form (y=mx+b). m=9, b=4 therefore y = 9x + 4 Number of people, x 1234 Total Cost, y$13$22$31$40

16. Page 221 Real-World Link 5. Graph the data Number of people, x 1234 Total Cost, y$13$22$31$40

17. Page 221 Real-World Link 5. Graph the data Number of people, x 1234 Total Cost, y$13$22$31$40

18. Page 222 The point-slope form of a linear equation. http://www.mathsisfun.com/algebra/line- equation-point-slope.html http://www.mathsisfun.com/algebra/line- equation-point-slope.html

19. Page 222 Write an equation in point-slope form for the line that passes through (-2,3) with a slope of 4. You have a point (-2,3) you have a slope 4 Plug it into point-slope y – y 1 =m(x - x 1 ) y – 3 = 4 (x - -2)then simplify y – 3 = 4(x + 2)

20. Page 222 Write the slope-intercept form of the equation for the line that passes through (-2,3) with a slope of 4. y – 3 = 4 (x - -2)then simplify y – 3 = 4(x + 2)use the distributive prop. y – 3 = 4x + 8 + 3 + 3add 3 to both sides y = 4x + 11slope-intercept form

21. Page 222 – Got It a You have 3 minutes to complete Got it problem a Get going!! You have a point (-1,2) and a slope -1/2 plug it into point-slope y – y 1 =m(x - x 1 ) y – 2=-1/2(x - -1) y – 2 = -1/2(x + 1)simplify y – 2 = - ½*x + ½use the distributive prop. + 2 + 2add 2 to both sides y = - ½ x + 2 ½ you have slope-intercept form

22. Page 223 Write an equation in point-slope form for the line that passes through (8,1) and (-2,9). You have two points all you can find is slope. m = (1-9)/(8- -2) = -8/10 = -4/5 Now I have a point (8,1) and a slope -4/5 I can plug it into point-slope y – y 1 =m(x - x 1 ).

23. Page 223 Write an equation in point-slope form for the line that passes through (8,1) and (-2,9). Now I have a point (8,1) and a slope -4/5 I can plug it into point-slope y – y 1 =m(x - x 1 ). y – 1 = -4/5 (x – 8) use the distributive prop. y – 1 = -4/5*x + 32/5 + 1 + 1 add 1 to both sides y = (-4/5)x + 37/5 you have slope-intercept

24. Page 223 – Got It c and d You have 3 minutes to complete Got it problem c Get going!! (3,0) and (6,-3)2 points – find slope m = (0 - -3)/(3 - 6) = 3/-3 = -1 Now I have a point (3,0) and a slope -1 so I can plug it into point-slope y – y 1 =m(x - x 1 ). y – 0=-1 (x - 3)use the distributive prop. y = -1x + 3 you have slope-intercept form

25. Page 223 – Got It c and d You have 3 minutes to complete Got it problem d Get going!! (-1,2) and (5,-10)2 points, find slope m = (2 - -10)/(-1 - 5) = 12/-6 = -2 Now I have a point (-1, 2) and a slope -2 so I can plug it into point-slope y – y 1 =m(x - x 1 ). y – 2=-2 (x - -1)simplify y – 2 = -2(x + 1)use the distributive prop. y – 2 = -2x – 2 + 2 + 2add 2 to both sides y = -2x you have slope-intercept form

26. Page 224 The cost of assistance dog training sessions is shown in the table. Write an equation in point-slope form to represent the cost y of attending x dog training sessions. Number of sessions – xCost - y 5165 10290 What do I have?

27. Page 224 Write an equation in point-slope form. I have two points I can find slope m = (165-290)/(5-10) = -125/-5 = 25 Now, I have a point (5,165) and a slope 25, I can plug it into point-slope y – y 1 =m(x - x 1 ). Number of sessions – xCost - y 5165 10290

28. Page 224 Write an equation in point-slope form. Now, I have a point (5,165) and a slope 25 I can plug it into point-slope y – y 1 =m(x - x 1 ). y – 165 = 25(x – 5) I am done!!! Number of sessions – xCost - y 5165 10290

29. Page 224 – Got It e You have 3 minutes to complete Got it problem e Get going!! The cost for making spirit buttons is shown in the table. Write an equation in point-slope form to represent the cost y of making x buttons. Number of buttons, x Cost, y 10025 15035 What do I have?

30. Page 224 – Got It e You have 3 minutes to complete Got it problem e Get going!! Write an equation in point-slope form to represent the cost y of making x buttons. I have two points I can find slope m = (25-35)/(100-150) = -10/-50 = 1/5 Now, I have a point (100,25) and a slope 1/5 I can plug it into point-slope y – y 1 =m(x - x 1 ). y – 25 = 1/5(x – 100) And I am DONE!! Number of buttons, x Cost, y 10025 15035

31. Page 224 Guided Practice I will work the odd You will work the even

32. Page 224 Guided Practice 1. point (2,5) and slope 4 I have a point and slope so I use point-slope y – y 1 =m(x - x 1 ). y – 5 = 4(x – 2)point-slope y – 5 = 4x – 8 y = 4x – 3slope-intercept

33. Page 224 Guided Practice 3. Janelle is planning a party. The cost for 20 people is $290. The cost for 45 people is $590. Write an equation in point-slope form to represent the cost y of having a party for x people. 20 people, 290 cost 45 people, 590 cost What do I have?

34. Page 224 Guided Practice 3. Write an equation in point-slope form 20 people, 290 cost 45 people, 590 cost I have two points I can find slope m = (290-590)/(20-45)=-300/-25=12 Now, I have a point (20,290) and a slope 12 I can plug it into point-slope y – y 1 =m(x - x 1 ). y – 290 = 12(x – 20) And I am DONE!!

35. Page 224 Guided Practice You do the even

36. Page 224 Guided Practice 2) y-1 = -2(x+3) and y = -2x-5 4) is it easier to substitute than to solve?

37. Homework 3.6 Independent Practice Pages 225-226 problems 1-14

38. Quick Review GivenFind Point & Slopey – y 1 =m(x - x 1 ) Slope & y-intercepty = mx + b Two points – Find slopem= (y 2 -y 1 )/(x 2 -x 1 )