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Mastering Linear Equations: Graphing and Functions <br>

Learn to plot points, draw scatter plots, graph linear equations, find the intercepts, and understand slope in this comprehensive guide. <br>

karolynr
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Mastering Linear Equations: Graphing and Functions <br>

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  1. Chapter 4 Notes Graphing Linear Equations and Functions

  2. 4.1 Coordinates and Scatter Plots Objectives: -Plot points in a coordinate plane -Draw scatter plots and make predictions about the data

  3. Terms • Coordinate Plane • Ordered pair • X-coordinate • Y-coordinate

  4. Labeling the Coordinate plane

  5. Plotting Points • Plot the following points • (0,3) • (-2, -1) • (2,0) • (4,5)

  6. Locating Quadrants Find the quadrant of the following points • (0,3) • (-2, -1) • (2,0) • (4,5)

  7. Making a Scatter Plot

  8. 4.2 Graphing Linear Equations Part1 Objectives: -Make a list of values for a given equation

  9. Terms • Solution of an Equation • Function Form

  10. Function Form • Rewrite the equations in function form (y=mx+b) • -3x + y = 12 • 2x + 3y = 6

  11. Function Form • Rewrite the equations in function form (y=mx+b) • -x – y = 5 • 5x + 5y = 20

  12. T-Charts • Rules for t-Charts • Equations must be in function form • Choose numbers for x • Substitute them in for x • Solve for y • Repeat to get a total of 3 values for your function

  13. T-Charts • Make a table of values(T-Chart) for each function • Y = -2x – 6 y = 3(6x – 1) X Y X Y

  14. T-Charts • Make a table of values(T-Chart) for each function • Y = 3x - 5 y = 7 – 4x X Y X Y

  15. When the equation has an X but no Y Ex: x = 5 When the equation has a y but no x Ex: y = 8 Special Cases

  16. 4.2 Graphing Linear Equations Part2 Objectives: -Graph linear equations and make t- charts

  17. T-Charts • Rules for t-Charts • Equations must be in function form • Choose numbers for x • Substitute them in for x • Solve for y • Graph the values

  18. Graphing • Y = 4x – 2 y = 2(x – 1) X Y X Y

  19. Graphing • 2x + 2y = 10 5x – 7 = 5y X Y X Y

  20. 4.3 Quick Graphs Using Intercepts Objectives: -Find the x and y intercepts -graph a linear equation using the x and y intercepts

  21. Terms • X- intercept • Y- intercept

  22. Finding the x-intercept • X-intercepts always have ordered pairs in the form (#,0) • To find the x-intercept you plug 0 in for y and solve for x.

  23. Finding the y-intercept • y-intercepts always have ordered pairs in the form (0,#) • To find the y-intercept you plug 0 in for x and solve for y.

  24. Practice • Given the x and y intercepts graph the equation • x-intercept = 2; x-intercept = -4; y-intercepts = -3 y-intercepts = 5

  25. 5x + 4y = -20 6x – y = 6 Finding x and y -intercept

  26. -3x + y = -6 3x – y = -2 Finding x and y -intercept

  27. 4.4 Slope Objectives: -Find the slope of a line given 2 pts

  28. Terms • Slope • Rate of change

  29. Finding Slope form a Graph A B

  30. Finding Slope with a Formula Slope = change in y change in x

  31. Special cases • #/0 means slope = undefined (U) • 0/# means slope = 0

  32. (2,3)(4,-5) (1,-5)(-5,2) (3,6)(3,0) (0,5)(7,5) Practice

  33. (4,1)(6,-3) (2,2)(-3,5) (-6,-1)(-6,-4) (0,-10)(-4,0) Practice

  34. White Board Practice • One person from each row get white boards and accessories

  35. 4.6 Quick Graphs Using Slope Intercept Objectives: -Graph a linear equation in slope intercept form

  36. Terms • Slope-intercept form • Parallel lines • Perpendicular Lines

  37. Locating slope and intercept • Given an equation in y=mx+b form • m=slope (pattern) b= y-intercept (start pt.) • Slope must be a fraction !!!

  38. How it works • 1st you start on the y axis at the b value • 2nd you use your slope to rise and run from the b value

  39. Graph each of the following and tell the slope and intercept Y = 2x – 3 Y= -3x – 2 Y= ½ x + 5 Practice

  40. Graph each of the following and tell the slope and intercept Y= 2/3x – 1 Y= 2x 2y + 3x = 6 Practice

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