2. Presentation Index Graphing Equations of Lines QUIZ: Graphing Equations of Lines

3. SORRY, incorrect answer! Try Again!

4. Chapter 2 Section 3 Graphing Linear Equations

5. What is a Linear Equation? A linear equation in two variables is an equation that can be written in standard form as Ax + By = C where A, B, and C are real numbers and A and B are not both 0.

6. Methods of Graphing 1)Table of Values 2) x- and y-intercepts 3) Slope-intercept form (y=mx+b)

7. Table of Values Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line. xy -4? -2? 0? 2? 4?

8. Table of Values y=3x+2 xy -4? -10 -2? -4 0? 2? 4? Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line. Y=3x+2 Y=3(-4)+2 Y= -12+2 Y= -10 Y=3x+2 Y=3(-2)+2 Y= -6+2 Y= -4 Use all the numbers!!

9. Table of Values Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line.

10. Table of Values Steps: 1.List 5 numbers (x) in the table. 2.Substitute each x into the equation to find y. 3.Plot all of the coordinates. 4.Connect the dots to make a line.

11. STOP! Work on the “ Try These ” #1-2 on the Note Sheet (You only need to do a table with three values)

12. Table of Values Practice: 1) y = 2x - 5 Does your graph look like this? #1

13. Table of Values Practice: 2) x + 3y = 6 Does your graph look like this? #2

14. x-intercept: The point where the line crosses the x-axis. –To find, let y = 0 and find the value of x. –Write as an ordered pair (x, 0) y-intercept: The point where the line crosses the y-axis. –To find, let x = 0 and find the value of y. –Write as an ordered pair (0, y) X- and Y-Intercepts What are they?

15. X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. x-intercept y=2x-6 0=2x-6 +6 +6 6=2x2 3=x x-intercept: (3,0) y=2x-6

16. X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. y=2x-6 y-intercept y=2x-6 y=2(0)-6 y=0-6 y= -6 y-intercept: (0,-6)

17. X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. y=2x-6 x-intercept: (3,0) y-intercept: (0,-6)

18. X- and Y-Intercepts Steps: 1)Find the x-intercept of the line (evaluate when y=0) 2)Find the y-intercept of the line (evaluate when x=0) 3)Plot the two ordered pairs (#,0) and (0,#) 4)Connect the dots to make a line. y=2x-6 x-intercept: (3,0) y-intercept: (0,-6)

19. STOP! Work on the “ Try These ” #1 – 2 on the Note Sheet

20. Practice: 1) y = 3x - 5 Does your graph look like this? X- and Y-Intercepts #1

21. Practice: 2) x + 2y = 6 Does your graph look like this? X- and Y-Intercepts #2

22. y=mx+b Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope-Intercept Form Slopey-intercept

23. -2x+y= -3 Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. +2x y=2x-3

24. Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. y=2x-3 Slope y-intercept Slope: 2 y-intercept: -3

25. Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y- intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope: 2 y-intercept: -3

26. Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope: 2 y-intercept: -3 Rise Run

27. Slope-Intercept Form Steps: 1.Set the equation equal to y (y=?). 2.Identify the slope and y-intercept. 3.Plot the y-intercept. 4.Use slope to count to the next point. 5.Connect the dots to make a line. Slope: 2 y-intercept: -3

28. STOP! Work on the “ Try These ” #1 – 2 on the Note Sheet

29. Practice: 1)Y = 2 / 3 x + 1 Does your graph look like this? Slope-Intercept Form #1

30. Practice: 2) 2x + y = 3 Does your graph look like this? Slope-Intercept Form #2

31. Vertical Lines 1)The x-coordinates of the points on a vertical line are the same. 2)The slope of any vertical line is undefined. 3)Equations of vertical lines are written x = the value of the x- coordinate. X = -5

32. 1)The y-coordinates of the points on a horizontal line are the same. 2)The slope of any horizontal line is 0. 3)Equations of horizontal lines are written y = the value of the y- coordinate. Horizontal Lines Y = 3

33. Graphing Review 1)Table of Values 2) X- and Y-Intercepts 3) Slope-Intercept form (y=mx+b)

34. Which of the following is NOT a Table of Values for y=2x-4? xy -4-12 -2-8 0-4 1-2 32 xy -5-14 -6 0-4 1-2 32 xy -5-14 -3-11 0-4 32 44 xy -2-8 -6 0-4 44 56 ABCD

35. What are the x- and y-intercepts? A B C D 2x+3y=6  (2,0) & (0,3)  (2,3) & (3,2)  (3,2) & (0,0)  (0,2) & (3,0)

36. Identify the slope and y-intercept. A B C D  Slope: -8, y-intercept: 7  Slope: -8, y-intercept: -7  Slope: 8, y-intercept: -7  Slope: 8, y-intercept: 7 8x+y= -7

37. Identify the graph of y= x-3 A B C D

38. Identify the graph of x+3y=9 ABCD A B C D

39. Great Job! You have completed the quiz. You may now begin your homework assignment.