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Mastering Linear Equations: Graphing Techniques and Practice Quiz

This presentation covers essential techniques for graphing linear equations, including the use of T-tables, x and y intercepts, and slope-intercept form (y = mx + b). You'll learn to identify intercepts, plot points, and construct lines through hands-on practice with various exercises. Additionally, a quiz at the end will test your understanding and reinforce key concepts. Ideal for students looking to strengthen their graphing skills and gain confidence in solving linear equations.

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Mastering Linear Equations: Graphing Techniques and Practice Quiz

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

  2. SORRY, incorrect answer!Try Again!

  3. Chapter 3Graphing Linear Equations

  4. 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.

  5. Methods of Graphing • T-Table • 2)x & y intercepts 3) Slope intercept form (y=mx+b)

  6. Steps: List 5 numbers (x) in the t-table. Plug each x into the equation to find y. Plot all of the coordinates. Connect the dots to make a line. T-Table

  7. y=3x+2 Steps: List 5 numbers (x) in the t-table. Plug each x into the equation to find y. Plot all of the coordinates. 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 Plug in all the numbers!! T-Table

  8. Steps: List 5 numbers (x) in the t-table. Plug each x into the equation to find y. Plot all of the coordinates. Connect the dots to make a line. T-Table

  9. Steps: List 5 numbers (x) in the t-table. Plug each x into the equation to find y. Plot all of the coordinates. Connect the dots to make a line. T-Table

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

  11. Practice: y=2x-5 Does your graph look like this? #1 T-Table

  12. Practice: x+3y=6 Does your graph look like this? #2 T-Table

  13. X & Y InterceptsWhat are they? • 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)

  14. 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=2x 2 3=x X-intercept: (3,0) X & Y Intercepts y=2x-6

  15. 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-Intercept y=2x-6 y=2(0)-6 y=0-6 y= -6 y-intercept: (0,-6) X & Y Intercepts y=2x-6

  16. 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 & Y Intercepts y=2x-6 x-intercept:(3,0) y-intercept: (0,-6)

  17. 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 & Y Intercepts y=2x-6 x-intercept:(3,0) y-intercept: (0,-6)

  18. STOP! Work on the “Try These” #3 – 4 on the Notesheet

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

  20. Practice: x+2y=6 Does your graph look like this? #2 X & Y Intercepts

  21. Horizontal Lines • The y-coordinates of the points on a horizontal line are the same. • The slope of any horizontal line is 0. • Equations of horizontal lines are written y = the value of the y-coordinate. Y = 5

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

  23. y=mx+b Steps: Set the equation equal to y (y=?) Identify the slope and y-intercept Plot the y-intercept Do the slope Connect the dots to make a line. Slope-Intercept Form Slope y-intercept

  24. -2x+y= -3 Steps: Set the equation equal to y (y=?) Identify the slope and y-intercept Plot the y-intercept Do the slope Connect the dots to make a line. Slope-Intercept Form +2x +2x y=2x-3

  25. Steps: Set the equation equal to y (y=?) Identify the slope and y-intercept Plot the y-intercept Do the slope Connect the dots to make a line. Slope-Intercept Form y=2x-3 Slope y-intercept Slope: 2 y-intercept: -3

  26. Steps: Set the equation equal to y (y=?) Identify the slope and y-intercept Plot the y-intercept Do the slope Connect the dots to make a line. Slope-Intercept Form Slope: 2 y-intercept: -3

  27. Steps: Set the equation equal to y (y=?) Identify the slope and y-intercept Plot the y-intercept Do the slope Connect the dots to make a line. Slope-Intercept Form Slope: 2 y-intercept: -3 Rise Run

  28. Steps: Set the equation equal to y (y=?) Identify the slope and y-intercept Plot the y-intercept Do the slope Connect the dots to make a line. Slope-Intercept Form Slope: 2 y-intercept: -3

  29. STOP! Work on the “Try These” #5 – 6 on the Notesheet

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

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

  32. Graphing Review • T-Table • 2)x & y intercepts 3) Slope intercept form (y=mx+b)

  33. Which of the following is NOT a T-Table for y=2x-4? A B C D

  34. 2x+3y=6 (2,0) & (0,3) (2,3) & (3,2) (3,2) & (0,0) (0,2) & (3,0) What is the x & y-intercept? A B C D

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

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

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

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

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